Correctly show sync status in continuous sync notification

diff --git a/lib/models/app_wallet.dart b/lib/models/app_wallet.dart
index e6da35c..9ae9f8f 100644
--- a/lib/models/app_wallet.dart
+++ b/lib/models/app_wallet.dart
@@ -118,3 +118,11 @@ abstract interface class AppWallet implements Listenable {
   Future<void> commitTx(AppPendingTx tx, String destinationAddress);
   Future<ResolvedOpenAlias?> resolveOpenAlias(String alias);
 }
+
+extension AppWalletSyncStatus on AppWallet {
+  /// Truly caught up: connected, synced, and a real height has loaded. The
+  /// height guard rules out the brief post-open window where `isSynced` flips
+  /// true before `syncedHeight` arrives (LWS reports 0 at first), which would
+  /// otherwise show "up to date" prematurely.
+  bool get isFullySynced => isConnected && isSynced && (syncedHeight ?? 0) > 0;
+}
diff --git a/lib/screens/wallet_home.dart b/lib/screens/wallet_home.dart
index da2e623..3473224 100644
--- a/lib/screens/wallet_home.dart
+++ b/lib/screens/wallet_home.dart
@@ -369,7 +369,7 @@ class _WalletHomeScreenState extends State<WalletHomeScreen> {
     var lwsConnectionIconStatus = StatusIconStatus.fail;
     var fiatApiIconStatus = StatusIconStatus.loading;
 
-    if (wallet.isConnected && wallet.isSynced && (wallet.syncedHeight ?? 0) > 0) {
+    if (wallet.isFullySynced) {
       lwsConnectionIconStatus = StatusIconStatus.complete;
     } else if (wallet.usingTor &&
             TorService.sharedInstance.status == TorConnectionStatus.connecting ||
diff --git a/lib/services/foreground_sync_service.dart b/lib/services/foreground_sync_service.dart
index 779d8d6..63dade6 100644
--- a/lib/services/foreground_sync_service.dart
+++ b/lib/services/foreground_sync_service.dart
@@ -61,9 +61,7 @@ class _SyncTaskHandler extends TaskHandler {
   void onRepeatEvent(DateTime timestamp) {
     final wallet = _wallet;
     final syncing =
-        wallet != null &&
-        wallet.connectionAddress.isNotEmpty &&
-        !(wallet.isConnected && wallet.isSynced);
+        wallet != null && wallet.connectionAddress.isNotEmpty && !wallet.isFullySynced;
     FlutterForegroundTask.updateService(
       notificationTitle: 'Skylight Wallet',
       notificationText: syncing ? 'Syncing…' : 'Wallet up to date',
@@ -118,14 +116,17 @@ void initForegroundSync() {
   );
 }
 
-Future<void> startForegroundSync() async {
+/// [synced] seeds the initial notification from the caller's live wallet state,
+/// so toggling this on while already caught up shows "up to date" immediately
+/// instead of a stale "Syncing…" until the isolate's first 30s tick.
+Future<void> startForegroundSync({bool synced = false}) async {
   if (!Platform.isAndroid) return;
   initForegroundSync();
   await FlutterForegroundTask.requestNotificationPermission();
   if (await FlutterForegroundTask.isRunningService) return;
   await FlutterForegroundTask.startService(
     notificationTitle: 'Skylight Wallet',
-    notificationText: 'Syncing…',
+    notificationText: synced ? 'Wallet up to date' : 'Syncing…',
     callback: foregroundSyncCallback,
   );
 }
diff --git a/lib/widgets/connection_settings_form.dart b/lib/widgets/connection_settings_form.dart
index fd77b46..07843ab 100644
--- a/lib/widgets/connection_settings_form.dart
+++ b/lib/widgets/connection_settings_form.dart
@@ -10,6 +10,7 @@ import 'package:skylight_wallet/services/tor_settings_service.dart';
 import 'package:skylight_wallet/util/logging.dart';
 
 import 'package:skylight_wallet/l10n/app_localizations.dart';
+import 'package:skylight_wallet/models/app_wallet.dart';
 import 'package:skylight_wallet/wallet_core_glue.dart';
 import 'package:skylight_wallet/services/tor_service.dart';
 
@@ -89,9 +90,11 @@ class _ConnectionSettingsFormState extends State<ConnectionSettingsForm> {
 
   void _setForegroundSyncEnabled(bool value) async {
     setState(() => _foregroundSyncEnabled = value);
+    // Captured before the await so the notification starts from the live status.
+    final synced = value && appWalletOf(context).isFullySynced;
     await SharedPreferencesService.set<bool>(SharedPreferencesKeys.foregroundSyncEnabled, value);
     if (value) {
-      await startForegroundSync();
+      await startForegroundSync(synced: synced);
     } else {
       await stopForegroundSync();
     }