ci: Update actions for queue merge validation (#11114)

## Summary

PR merge queue was enabled but actions were not updated to trigger on
`merge_group`:

https://docs.github.com/en/repositories/configuring-branches-and-merges-in-your-repository/configuring-pull-request-merges/managing-a-merge-queue#triggering-merge-group-checks-with-github-actions

## Changes

- **What**: 
- `.github/actions/lint-format-verify/action.yml` extrated shared Verify
lint and format steps
- `.github/workflows/ci-lint-format.yaml` updated to use shared
composite action
- `.github/workflows/ci-lint-format-queue.yaml` new action that triggers
on merge_group to validate format
- `.github/workflows/ci-tests-e2e.yaml` triggers on merge_group
- `.github/workflows/ci-tests-unit.yaml` triggers on merge_group

## Review Focus

<!-- Critical design decisions or edge cases that need attention -->

<!-- If this PR fixes an issue, uncomment and update the line below -->
<!-- Fixes #ISSUE_NUMBER -->

## Screenshots (if applicable)

<!-- Add screenshots or video recording to help explain your changes -->

┆Issue is synchronized with this [Notion
page](https://www.notion.so/PR-11114-ci-Update-actions-for-queue-merge-validation-33e6d73d3650815f8c88f40736b513ec)
by [Unito](https://www.unito.io)

.github/actions/lint-format-verify/action.yml

@@ -0,0 +1,31 @@
+name: 'Lint and format verify'
+description: >
+  Runs the lint/format/knip verification suite plus a conditional
+  browser-tests typecheck. Shared by ci-lint-format.yaml (PR) and
+  ci-lint-format-queue.yaml (merge queue) so both paths run the exact
+  same checks. The caller is responsible for checkout and frontend setup
+  before invoking this action.
+
+runs:
+  using: composite
+  steps:
+    - name: Detect browser_tests changes
+      id: changed-paths
+      uses: dorny/paths-filter@de90cc6fb38fc0963ad72b210f1f284cd68cea36 # v3.0.2
+      with:
+        filters: |
+          browser_tests:
+            - 'browser_tests/**'
+
+    - name: Verify lint and format
+      shell: bash
+      run: |
+        pnpm lint
+        pnpm stylelint
+        pnpm format:check
+        pnpm knip
+
+    - name: Typecheck browser tests
+      if: steps.changed-paths.outputs.browser_tests == 'true'
+      shell: bash
+      run: pnpm typecheck:browser

.github/workflows/ci-lint-format-queue.yaml

@@ -0,0 +1,29 @@
+# Description: Lint and format verification for GitHub merge queue runs.
+# Paired with ci-lint-format.yaml — workflow name and job name must match
+# so branch protection resolves a single required check in both the
+# pull_request and merge_group contexts. This file runs verify-only steps
+# with a read-only token; auto-fix and PR comments live in the PR workflow.
+name: 'CI: Lint Format'
+
+on:
+  merge_group:
+
+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: true
+
+permissions:
+  contents: read
+
+jobs:
+  lint-and-format:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout merge group ref
+        uses: actions/checkout@v6
+
+      - name: Setup frontend
+        uses: ./.github/actions/setup-frontend
+
+      - name: Verify lint and format
+        uses: ./.github/actions/lint-format-verify

.github/workflows/ci-lint-format.yaml

@@ -1,4 +1,7 @@
-# Description: Linting and code formatting validation for pull requests
+# Description: Linting and code formatting validation for pull requests.
+# Paired with ci-lint-format-queue.yaml - workflow name and job name must
+# match so branch protection resolves a single required check in both the
+# pull_request and merge_group contexts.
 name: 'CI: Lint Format'
 
 on:
@@ -26,14 +29,6 @@ jobs:
       - name: Setup frontend
         uses: ./.github/actions/setup-frontend
 
-      - name: Detect browser_tests changes
-        id: changed-paths
-        uses: dorny/paths-filter@de90cc6fb38fc0963ad72b210f1f284cd68cea36 # v3.0.2
-        with:
-          filters: |
-            browser_tests:
-              - 'browser_tests/**'
-
       - name: Run ESLint with auto-fix
         run: pnpm lint:fix
 
@@ -77,16 +72,8 @@ jobs:
           echo "See CONTRIBUTING.md for more details."
           exit 1
 
-      - name: Final validation
-        run: |
-          pnpm lint
-          pnpm stylelint
-          pnpm format:check
-          pnpm knip
-
-      - name: Typecheck browser tests
-        if: steps.changed-paths.outputs.browser_tests == 'true'
-        run: pnpm typecheck:browser
+      - name: Verify lint and format
+        uses: ./.github/actions/lint-format-verify
 
       - name: Comment on PR about auto-fix
         if: steps.verify-changed-files.outputs.changed == 'true' && github.event.pull_request.head.repo.full_name == github.repository

.github/workflows/ci-tests-e2e.yaml

@@ -8,6 +8,7 @@ on:
   pull_request:
     branches-ignore: [wip/*, draft/*, temp/*]
     paths-ignore: ['**/*.md']
+  merge_group:
   workflow_dispatch:
 
 concurrency:

.github/workflows/ci-tests-unit.yaml

@@ -8,6 +8,7 @@ on:
   pull_request:
     branches-ignore: [wip/*, draft/*, temp/*]
     paths-ignore: ['**/*.md']
+  merge_group:
 
 concurrency:
   group: ${{ github.workflow }}-${{ github.ref }}