ci: add a dart format gate and fix the one drifted test file

Format drift was unchecked in CI. Add the gate before analyze and include integration_test in the documented format commands.

.github/PULL_REQUEST_TEMPLATE.md

@@ -19,7 +19,7 @@
 
 <!-- Check only commands relevant to this change. Explain skipped checks below. -->
 
-- [ ] `dart format --output=none --set-exit-if-changed lib test`
+- [ ] `dart format --output=none --set-exit-if-changed lib test integration_test`
 - [ ] `flutter analyze`
 - [ ] `flutter test`
 - [ ] `bash scripts/check_rust_backend.sh`

.github/workflows/ci.yml

@@ -118,6 +118,9 @@ jobs:
       - name: Get Flutter dependencies
         run: flutter pub get
 
+      - name: Check formatting
+        run: dart format --output=none --set-exit-if-changed lib test integration_test
+
       - name: Analyze
         run: flutter analyze