Add CI job to check API docs

This ensures that `cargo doc` does not generate any warnings.

.github/workflows/main.yml

@@ -98,6 +98,18 @@ jobs:
       - run: rustup component add clippy
       - run: cargo clippy --workspace --all-targets --no-deps -- -D warnings
 
+  docs:
+    name: Check API docs
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - name: Install Rust
+        run: bash ci/install-rust.sh stable x86_64-unknown-linux-gnu
+      - name: Ensure intradoc links are valid
+        run: cargo doc --workspace --document-private-items --no-deps
+        env:
+          RUSTDOCFLAGS: -D warnings
+
   # The success job is here to consolidate the total success/failure state of
   # all other jobs. This job is then included in the GitHub branch protection
   # rule which prevents merges unless all other jobs are passing. This makes
@@ -112,6 +124,7 @@ jobs:
       - aarch64-cross-builds
       - gui
       - clippy
+      - docs
     runs-on: ubuntu-latest
     steps:
       - run: jq --exit-status 'all(.result == "success")' <<< '${{ toJson(needs) }}'