Add a CI job to emulate docs.rs builds

diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index 2190dd5..cbc50ba 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -233,6 +233,24 @@ jobs:
           RUSTFLAGS: '--cfg=taproot'
           RUSTDOCFLAGS: '--cfg=taproot'
 
+  check_docs:
+    runs-on: self-hosted
+    env:
+      # While docs.rs builds using a nightly compiler (and we use some nightly features),
+      # nightly ends up randomly breaking builds occasionally, so we instead use beta
+      # and set RUSTC_BOOTSTRAP in check-docsrs.sh
+      TOOLCHAIN: beta
+    steps:
+      - name: Checkout source code
+        uses: actions/checkout@v4
+        with:
+          fetch-depth: 0
+      - name: Install Rust ${{ env.TOOLCHAIN }} toolchain
+        run: |
+          curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh -s -- -y --profile=minimal --default-toolchain ${{ env.TOOLCHAIN }}
+      - name: Simulate docs.rs build
+        run: ci/check-docsrs.sh
+
   fuzz:
     runs-on: self-hosted
     env:
diff --git a/ci/check-docsrs.sh b/ci/check-docsrs.sh
new file mode 100755
index 0000000..b8776f8
--- /dev/null
+++ b/ci/check-docsrs.sh
@@ -0,0 +1,42 @@
+#!/bin/bash
+#shellcheck disable=SC2002,SC2086,SC2207
+
+set -ex
+
+# Attempt to simulate the docsrs builds. Sadly its not entirely trivial as
+# docs.rs reads metadata out of Cargo.toml which we don't want to have a whole
+# parser for.
+
+WORKSPACE_MEMBERS=( $(cat Cargo.toml | tr '\n' '\r' | sed 's/\r    //g' | tr '\r' '\n' | grep '^members =' | sed 's/members.*=.*\[//' | tr -d '"' | tr ',' '\n') )
+echo "${WORKSPACE_MEMBERS[@]}"
+for CRATE in "${WORKSPACE_MEMBERS[@]}"; do
+	pushd "$CRATE"
+	CARGO_ARGS=""
+	RUSTDOC_ARGS=""
+	cat Cargo.toml | grep -A 100 '\[package.metadata.docs.rs\]' | tail -n +2 > /tmp/ldk-docsrs-rustdoc-config.txt
+	while read -r LINE; do
+		case "$LINE" in
+			"["*) break;;
+			"features"*)
+				OG_IFS="$IFS"
+				IFS=','
+				for FEATURE in $(echo "$LINE" | sed 's/features.*=.*\[//g' | tr -d '"] '); do
+					export CARGO_ARGS="$CARGO_ARGS --features $FEATURE"
+				done
+				IFS="$OG_IFS"
+				;;
+			"all-features = true")
+				export CARGO_ARGS="$CARGO_ARGS --all-features"
+				;;
+			"rustdoc-args"*)
+				RUSTDOC_ARGS="$(echo "$LINE" | sed 's/rustdoc-args.*=.*\[//g' | tr -d '"],')"
+				;;
+		esac
+	done < /tmp/ldk-docsrs-rustdoc-config.txt
+	rm /tmp/ldk-docsrs-rustdoc-config.txt
+	echo "Building $CRATE with args $CARGO_ARGS and flags $RUSTDOC_ARGS"
+	# We rely on nightly features but want to use a stable release in CI to avoid
+	# spurous breakage, thus we set RUSTC_BOOTSTRAP=1 here.
+	RUSTC_BOOTSTRAP=1 cargo rustdoc $CARGO_ARGS -- $RUSTDOC_ARGS
+	popd
+done
diff --git a/ci/ci-tests.sh b/ci/ci-tests.sh
index f784140..c3637ab 100755
--- a/ci/ci-tests.sh
+++ b/ci/ci-tests.sh
@@ -1,4 +1,5 @@
 #!/bin/bash
+#shellcheck disable=SC2002,SC2207
 set -eox pipefail
 
 RUSTC_MINOR_VERSION=$(rustc --version | awk '{ split($2,a,"."); print a[2] }')
@@ -41,23 +42,7 @@ export RUST_BACKTRACE=1
 echo -e "\n\nChecking the workspace, except lightning-transaction-sync."
 cargo check --verbose --color always
 
-# When the workspace members change, make sure to update the list here as well
-# as in `Cargo.toml`.
-WORKSPACE_MEMBERS=(
-	lightning
-	lightning-types
-	lightning-block-sync
-	lightning-invoice
-	lightning-net-tokio
-	lightning-persister
-	lightning-background-processor
-	lightning-rapid-gossip-sync
-	lightning-custom-message
-	lightning-macros
-	lightning-dns-resolver
-	lightning-liquidity
-	possiblyrandom
-)
+WORKSPACE_MEMBERS=( $(cat Cargo.toml | tr '\n' '\r' | sed 's/\r    //g' | tr '\r' '\n' | grep '^members =' | sed 's/members.*=.*\[//' | tr -d '"' | tr ',' ' ') )
 
 echo -e "\n\nTesting the workspace, except lightning-transaction-sync."
 cargo test --verbose --color always