Add a workflow to update the rush shrinkwrap file

.github/workflows/update-rush-shrinkwrap.yml

@@ -0,0 +1,47 @@
+name: Update Rush Shrinkwrap
+
+on:
+  pull_request:
+    types: [opened, synchronize, reopened]
+  workflow_dispatch:
+
+jobs:
+  update-shrinkwrap:
+    runs-on: ubuntu-latest
+    permissions:
+      contents: write
+      pull-requests: write
+
+    steps:
+      - name: Checkout repository
+        uses: actions/checkout@v6
+        with:
+          token: ${{ secrets.GITHUB_TOKEN }}
+          ref: ${{ github.head_ref || github.ref_name }}
+          fetch-depth: 0
+
+      - name: Setup Node.js
+        uses: actions/setup-node@v6
+        with:
+          node-version: '20'
+
+      - name: Rush update
+        run: node common/scripts/install-run-rush.js update --full
+
+      - name: Check for changes
+        id: check_changes
+        run: |
+          if git diff --quiet common/config/rush/npm-shrinkwrap.json; then
+            echo "has_changes=false" >> $GITHUB_OUTPUT
+          else
+            echo "has_changes=true" >> $GITHUB_OUTPUT
+          fi
+
+      - name: Commit and push changes
+        if: steps.check_changes.outputs.has_changes == 'true'
+        run: |
+          git config user.name "github-actions[bot]"
+          git config user.email "github-actions[bot]@users.noreply.github.com"
+          git add common/config/rush/npm-shrinkwrap.json
+          git commit -m "chore: update rush npm-shrinkwrap"
+          git push