feat(core/caesar): allow back in multishare setup

### core/embed/rust/src/ui/layout_caesar/component/input_methods/number_input.rs
@@ -1,10 +1,19 @@
-use super::super::{ButtonLayout, ChoiceFactory, ChoiceItem, ChoiceMsg, ChoicePage};
+use super::super::{theme, ButtonLayout, ChoiceFactory, ChoiceItem, ChoiceMsg, ChoicePage};
 use crate::strutil::ShortString;
 use crate::translations::TR;
 use crate::ui::component::{Component, Event, EventCtx};
 use crate::ui::geometry::Rect;
 use crate::ui::shape::Renderer;
 
+/// Action of a single choice in the number input carousel: either a number
+/// from the offered range, or going back to the previous screen (the leftmost
+/// item).
+#[derive(Clone, Copy)]
+pub enum NumberInputAction {
+    Back,
+    Number(u32),
+}
+
 struct ChoiceFactoryNumberInput {
     min: u32,
     max: u32,
@@ -17,45 +26,60 @@ impl ChoiceFactoryNumberInput {
 }
 
 impl ChoiceFactory for ChoiceFactoryNumberInput {
-    type Action = u32;
+    type Action = NumberInputAction;
     type Item = ChoiceItem;
 
     fn count(&self) -> usize {
-        (self.max - self.min + 1) as usize
+        // one extra item for going back
+        (self.max - self.min + 2) as usize
     }
 
     fn get(&self, choice_index: usize) -> (Self::Item, Self::Action) {
-        let num = self.min + choice_index as u32;
-        let text = unwrap!(ShortString::try_from(num));
-        let mut choice_item = ChoiceItem::new(
-            text,
-            ButtonLayout::arrow_armed_arrow(TR::buttons__select.into()),
-        );
-
-        // Disabling prev/next buttons for the first/last choice.
-        // (could be done to the same button if there is only one)
         if choice_index == 0 {
-            choice_item.set_left_btn(None);
-        }
-        if choice_index == <ChoiceFactoryNumberInput as ChoiceFactory>::count(self) - 1 {
-            choice_item.set_right_btn(None);
-        }
+            // the leftmost item goes back to the previous screen when
+            // confirmed; there is no going further left from it
+            (
+                TR::inputs__back.map_translated(|t| {
+                    let mut choice_item = ChoiceItem::new(
+                        t,
+                        ButtonLayout::arrow_armed_arrow(TR::buttons__select.into()),
+                    )
+                    .with_icon(theme::ICON_ARROW_BACK_UP);
+                    choice_item.set_left_btn(None);
+                    choice_item
+                }),
+                NumberInputAction::Back,
+            )
+        } else {
+            let num = self.min + choice_index as u32 - 1;
+            let text = unwrap!(ShortString::try_from(num));
+            let mut choice_item = ChoiceItem::new(
+                text,
+                ButtonLayout::arrow_armed_arrow(TR::buttons__select.into()),
+            );
+
+            // Disabling the next button for the last choice.
+            if choice_index == <ChoiceFactoryNumberInput as ChoiceFactory>::count(self) - 1 {
+                choice_item.set_right_btn(None);
+            }
 
-        (choice_item, num)
+            (choice_item, NumberInputAction::Number(num))
+        }
     }
 }
 
 /// Simple wrapper around `ChoicePage` that allows for
 /// inputting a list of values and receiving the chosen one.
 pub struct NumberInput {
-    choice_page: ChoicePage<ChoiceFactoryNumberInput, u32>,
+    choice_page: ChoicePage<ChoiceFactoryNumberInput, NumberInputAction>,
     min: u32,
 }
 
 impl NumberInput {
     pub fn new(min: u32, max: u32, init_value: u32) -> Self {
         let choices = ChoiceFactoryNumberInput::new(min, max);
-        let initial_page = init_value - min;
+        // +1 to skip the leading "back" item
+        let initial_page = init_value - min + 1;
         Self {
             min,
             choice_page: ChoicePage::new(choices).with_initial_page_counter(initial_page as usize),
@@ -64,7 +88,7 @@ impl NumberInput {
 }
 
 impl Component for NumberInput {
-    type Msg = ChoiceMsg<u32>;
+    type Msg = ChoiceMsg<NumberInputAction>;
 
     fn place(&mut self, bounds: Rect) -> Rect {
         self.choice_page.place(bounds)

### core/embed/rust/src/ui/layout_caesar/component/mod.rs
@@ -54,7 +54,7 @@ pub use frame::{Frame, ScrollableFrame};
 pub use homescreen::{check_homescreen_format, ConfirmHomescreen, Homescreen, Lockscreen};
 #[cfg(feature = "translations")]
 pub use input_methods::{
-    number_input::NumberInput,
+    number_input::{NumberInput, NumberInputAction},
     passphrase::PassphraseEntry,
     pin::PinEntry,
     simple_choice::{SimpleChoice, MAX_LENGTH as SIMPLE_CHOICE_MAX_LENGTH},

### core/embed/rust/src/ui/layout_caesar/component_msg_obj.rs
@@ -2,16 +2,18 @@ use core::convert::TryInto;
 
 use super::component::{
     AddressDetails, ButtonPage, CancelConfirmMsg, CancelInfoConfirmMsg, CoinJoinProgress,
-    ConfirmHomescreen, Flow, Frame, Homescreen, Lockscreen, NumberInput, Page, PassphraseEntry,
-    PinEntry, Progress, ScrollableFrame, ShowMore, WordlistEntry,
+    ConfirmHomescreen, Flow, Frame, Homescreen, Lockscreen, NumberInput, NumberInputAction, Page,
+    PassphraseEntry, PinEntry, Progress, ScrollableFrame, ShowMore, WordlistEntry,
 };
 use crate::micropython::{Error, Obj};
 use crate::ui::component::base::Component;
 use crate::ui::component::paginated::{PageMsg, Paginate};
-use crate::ui::component::text::paragraphs::{ParagraphSource, Paragraphs};
-use crate::ui::component::{Never, Timeout};
+use crate::ui::component::text::paragraphs::{
+    Checklist, ParagraphSource, ParagraphVecLong, Paragraphs,
+};
+use crate::ui::component::{FlowMsg, MsgMap, Never, Timeout};
 use crate::ui::layout::obj::ComponentMsgObj;
-use crate::ui::layout::result::{CANCELLED, CONFIRMED, INFO};
+use crate::ui::layout::result::{BACK, CANCELLED, CONFIRMED, INFO};
 
 impl From<CancelConfirmMsg> for Obj {
     fn from(value: CancelConfirmMsg) -> Self {
@@ -111,11 +113,31 @@ impl ComponentMsgObj for NumberInput {
     fn msg_try_into_obj(&self, msg: Self::Msg) -> Result<Obj, Error> {
         match msg {
             Self::Msg::Cancel => (CANCELLED.as_obj(), 0).try_into(),
-            Self::Msg::Choice { item, .. } => (CONFIRMED.as_obj(), item).try_into(),
+            Self::Msg::Choice {
+                item: NumberInputAction::Back,
+                ..
+            } => (BACK.as_obj(), 0).try_into(),
+            Self::Msg::Choice {
+                item: NumberInputAction::Number(n),
+                ..
+            } => (CONFIRMED.as_obj(), n).try_into(),
         }
     }
 }
 
+/// Layout returned by `show_checklist`: the checklist of backup steps with an
+/// optional back button (up arrow) in place of the cancel button.
+pub type ChecklistScreen =
+    MsgMap<ButtonPage<Checklist<ParagraphVecLong<'static>>>, fn(PageMsg<Never>) -> Option<FlowMsg>>;
+
+impl ComponentMsgObj for ChecklistScreen {
+    fn msg_try_into_obj(&self, msg: Self::Msg) -> Result<Obj, Error> {
+        // `TryFrom<FlowMsg> for Obj` covers all the emitted variants,
+        // including `FlowMsg::Back`.
+        msg.try_into()
+    }
+}
+
 impl ComponentMsgObj for WordlistEntry {
     fn msg_try_into_obj(&self, msg: Self::Msg) -> Result<Obj, Error> {
         msg.try_into()

### core/embed/rust/src/ui/layout_caesar/ui_firmware.rs
@@ -24,7 +24,8 @@ use crate::ui::component::text::paragraphs::{
 };
 use crate::ui::component::text::TextStyle;
 use crate::ui::component::{
-    Component, ComponentExt, Empty, FormattedText, Label, LineBreaking, Paginate, Timeout,
+    Component, ComponentExt, Empty, FlowMsg, FormattedText, Label, LineBreaking, Never, PageMsg,
+    Paginate, Timeout,
 };
 use crate::ui::layout::obj::{LayoutMaybeTrace, LayoutObj, RootComponent};
 use crate::ui::layout::util::{ConfirmValueParams, PropsList, RecoveryType};
@@ -1004,7 +1005,7 @@ impl FirmwareUI for UICaesar {
         button: TString<'static>,
         active: usize,
         items: [TString<'static>; MAX_CHECKLIST_ITEMS],
-        _back_button: bool,
+        back_button: bool,
     ) -> Result<impl LayoutMaybeTrace, Error> {
         let mut paragraphs = ParagraphVecLong::new();
         for (i, item) in items.into_iter().enumerate() {
@@ -1016,6 +1017,16 @@ impl FirmwareUI for UICaesar {
             paragraphs.add(Paragraph::new(style, item));
         }
         let confirm_btn = Some(ButtonDetails::text(button));
+        // The left button (only present when `back_button` is set) emits
+        // `PageMsg::Cancelled`; interpret it as going back. Going back is the
+        // only way out of the checklist -- interrupting the flow is not
+        // possible.
+        let cancel_btn = back_button.then(ButtonDetails::up_arrow_icon);
+        let map_fn: fn(PageMsg<Never>) -> Option<FlowMsg> = |msg| match msg {
+            PageMsg::Cancelled => Some(FlowMsg::Back),
+            PageMsg::Confirmed => Some(FlowMsg::Confirmed),
+            _ => None,
+        };
 
         let layout = RootComponent::new(
             ButtonPage::new(
@@ -1031,7 +1042,9 @@ impl FirmwareUI for UICaesar {
                 .with_current_offset(theme::CHECKLIST_CURRENT_OFFSET),
                 theme::BG,
             )
-            .with_confirm_btn(confirm_btn),
+            .with_confirm_btn(confirm_btn)
+            .with_cancel_btn(cancel_btn)
+            .map(map_fn),
         );
         Ok(layout)
     }

### core/src/trezor/ui/layouts/caesar/reset.py
@@ -3,6 +3,7 @@
 import trezorui_api
 from trezor import TR
 from trezor.enums import ButtonRequestType
+from trezor.wire import ActionCancelled
 
 from ..common import interact
 from . import confirm_action, show_success, show_warning
@@ -125,6 +126,7 @@ async def slip39_show_checklist(
         button=TR.buttons__continue,
         active=step,
         items=items,
+        back_button=back_button,
     ) as layout:
         return await interact(layout, "slip39_checklist", ButtonRequestType.ResetDevice)
 
@@ -135,7 +137,7 @@ async def _prompt_number(
     min_count: int,
     max_count: int,
     br_name: str,
-) -> int:
+) -> int | trezorui_api.UiResult:
     with trezorui_api.request_number(
         title=title,
         count=count,
@@ -146,14 +148,21 @@ async def _prompt_number(
             num_input,
             br_name,
             ButtonRequestType.ResetDevice,
+            raise_on_cancel=None,
         )
 
+    if result is trezorui_api.CANCELLED:
+        # not reachable from the UI, only via debuglink
+        raise ActionCancelled
+
     if __debug__:
         if isinstance(result, str):
             # debuglink for TR sends a string representing the number
             result = CONFIRMED, int(result)
     status, value = result
 
+    if status is trezorui_api.BACK:
+        return trezorui_api.BACK
     assert status is CONFIRMED
     assert isinstance(value, int)
     return value

### tests/click_tests/test_repeated_backup.py
@@ -145,8 +145,8 @@ def test_repeated_backup_via_device(
     reset.set_selection(debug, 3 - 5)
     # confirm checklist
     reset.confirm_read(debug)
-    # threshold=2
-    reset.set_selection(debug, 2 - 3)
+    # threshold=2 (the default for 3 shares)
+    reset.set_selection(debug, 0)
     # confirm checklist
     reset.confirm_read(debug)
     # confirm backup warning

### tests/device_tests/test_msg_backup_device.py
@@ -190,7 +190,7 @@ def test_backup_slip39_advanced(
     assert expected_ms == actual_ms
 
 
-@pytest.mark.models("delizia,eckhart")  # going back is supported on these layouts
+@pytest.mark.models("safe3,delizia,eckhart")  # going back is supported on these layouts
 @pytest.mark.setup_client(needs_backup=True, mnemonic=MNEMONIC_SLIP39_BASIC_20_3of6)
 def test_backup_slip39_basic_back_navigation(
     session: Session, backup_method: messages.BackupMethod
@@ -216,7 +216,7 @@ def test_backup_slip39_basic_back_navigation(
     assert expected_ms == actual_ms
 
 
-@pytest.mark.models("delizia,eckhart")  # going back is supported on these layouts
+@pytest.mark.models("safe3,delizia,eckhart")  # going back is supported on these layouts
 @pytest.mark.setup_client(needs_backup=True, mnemonic=MNEMONIC_SLIP39_ADVANCED_20)
 def test_backup_slip39_advanced_back_navigation(
     session: Session, backup_method: messages.BackupMethod

### tests/input_flows.py
@@ -2730,6 +2730,75 @@ def __init__(
         self.mnemonics: list[str] = []
         self.method = method
 
+    def input_flow_caesar(self) -> BRGeneratorType:
+        assert self.method is messages.BackupMethod.Display
+
+        yield  # Backup intro
+        self.debug.press_yes()
+
+        # checklist: set number of shares (no going back from the first step)
+        assert (yield).name == "slip39_checklist"
+        self.debug.press_yes()
+
+        # number of shares info
+        assert (yield).name == "slip39_shares"
+        self.debug.press_yes()
+
+        # number of shares carousel: navigate to the BACK item and select it
+        assert (yield).name == "slip39_shares"
+        for _ in range(5):  # initial value 5 -> 5 items to the left
+            self.debug.press_left()
+        self.debug.press_middle()
+
+        # checklist: set number of shares
+        assert (yield).name == "slip39_checklist"
+        self.debug.press_yes()
+
+        # number of shares info
+        assert (yield).name == "slip39_shares"
+        self.debug.press_yes()
+
+        # number of shares carousel: change the default 5 to 3
+        assert (yield).name == "slip39_shares"
+        self.debug.press_left()
+        self.debug.press_left()
+        self.debug.press_middle()
+
+        # checklist: set threshold
+        assert (yield).name == "slip39_checklist"
+        self.debug.press_yes()
+
+        # threshold info
+        assert (yield).name == "slip39_prompt_threshold"
+        self.debug.press_yes()
+
+        # threshold carousel: change the default 2 to 3
+        assert (yield).name == "slip39_threshold"
+        self.debug.press_right()
+        self.debug.press_middle()
+
+        # checklist: write down the shares -- go back via the up arrow
+        assert (yield).name == "slip39_checklist"
+        self.debug.press_left()
+
+        # threshold info
+        assert (yield).name == "slip39_prompt_threshold"
+        self.debug.press_yes()
+
+        # threshold carousel: the previously entered 3 is preselected
+        assert (yield).name == "slip39_threshold"
+        self.debug.press_middle()
+
+        # checklist: write down the shares
+        assert (yield).name == "slip39_checklist"
+        self.debug.press_yes()
+
+        yield  # Confirm show seeds
+        self.debug.press_yes()
+
+        # Mnemonic phrases
+        self.mnemonics = yield from load_N_shares(self.debug, 3, self.method)
+
     def input_flow_delizia(self) -> BRGeneratorType:
         assert self.method in (
             messages.BackupMethod.Display,
@@ -2893,6 +2962,115 @@ def __init__(
         self.mnemonics: list[list[str]] = []
         self.method = method
 
+    def input_flow_caesar(self) -> BRGeneratorType:
+        assert self.method is messages.BackupMethod.Display
+
+        yield  # Backup intro
+        self.debug.press_yes()
+
+        # checklist: set number of groups (no going back from the first step)
+        assert (yield).name == "slip39_checklist"
+        self.debug.press_yes()
+
+        # number of groups carousel: change the default 5 to 2
+        assert (yield).name == "slip39_groups"
+        for _ in range(3):  # 5 -> 2
+            self.debug.press_left()
+        self.debug.press_middle()
+
+        # checklist: set group threshold
+        assert (yield).name == "slip39_checklist"
+        self.debug.press_yes()
+
+        # group threshold carousel: keep the default 2
+        assert (yield).name == "slip39_group_threshold"
+        self.debug.press_middle()
+
+        # checklist: set sizes and thresholds of the groups
+        assert (yield).name == "slip39_checklist"
+        self.debug.press_yes()
+
+        # group 1 shares info
+        assert (yield).name == "slip39_shares"
+        self.debug.press_yes()
+
+        # group 1 shares carousel: change the default 5 to 3
+        assert (yield).name == "slip39_shares"
+        self.debug.press_left()
+        self.debug.press_left()
+        self.debug.press_middle()
+
+        # group 1 threshold info
+        assert (yield).name == "slip39_prompt_threshold"
+        self.debug.press_yes()
+
+        # group 1 threshold carousel: keep the default 2
+        assert (yield).name == "slip39_threshold"
+        self.debug.press_middle()
+
+        # group 2 shares info
+        assert (yield).name == "slip39_shares"
+        self.debug.press_yes()
+
+        # group 2 shares carousel: navigate to the BACK item and select it
+        assert (yield).name == "slip39_shares"
+        for _ in range(5):  # initial value 5 -> 5 items to the left
+            self.debug.press_left()
+        self.debug.press_middle()
+
+        # group 1 threshold info (again, after going back)
+        assert (yield).name == "slip39_prompt_threshold"
+        self.debug.press_yes()
+
+        # group 1 threshold carousel: the previously entered 2 is preselected
+        assert (yield).name == "slip39_threshold"
+        self.debug.press_middle()
+
+        # group 2 shares info
+        assert (yield).name == "slip39_shares"
+        self.debug.press_yes()
+
+        # group 2 shares carousel: keep the default 5
+        assert (yield).name == "slip39_shares"
+        self.debug.press_middle()
+
+        # group 2 threshold info
+        assert (yield).name == "slip39_prompt_threshold"
+        self.debug.press_yes()
+
+        # group 2 threshold carousel: change the default 3 to 4, then navigate
+        # to the BACK item and select it
+        assert (yield).name == "slip39_threshold"
+        self.debug.press_right()  # 3 -> 4
+        for _ in range(3):  # 4 is the third item -> 3 items to the left
+            self.debug.press_left()
+        self.debug.press_middle()
+
+        # group 2 shares info
+        assert (yield).name == "slip39_shares"
+        self.debug.press_yes()
+
+        # group 2 shares carousel: the previously entered 5 is preselected
+        assert (yield).name == "slip39_shares"
+        self.debug.press_middle()
+
+        # group 2 threshold info
+        assert (yield).name == "slip39_prompt_threshold"
+        self.debug.press_yes()
+
+        # group 2 threshold carousel: the default 3 is shown again -- keep it
+        assert (yield).name == "slip39_threshold"
+        self.debug.press_middle()
+
+        yield  # Confirm show seeds
+        self.debug.press_yes()
+
+        # Mnemonic phrases - show & confirm shares for all groups
+        # 2 groups: 2-of-3 and 3-of-5
+        self.mnemonics = yield from load_N_groups(
+            self.debug, [(2, 3), (3, 5)], self.method
+        )
+
     def input_flow_delizia(self) -> BRGeneratorType:
         assert self.method in (
             messages.BackupMethod.Display,