fix: Use RELEASE_PAT for checkout in release-update-adk-web workflow

This resolves a token conflict where actions/checkout persisted the default
GITHUB_TOKEN, causing subsequent git push operations by create-pull-request
(which uses RELEASE_PAT) to fail with a 400 Bad Request.

Co-authored-by: Yifan Wang <wanyif@google.com>
PiperOrigin-RevId: 943541293

Author: wyf7107

.github/workflows/release-update-adk-web.yaml

@@ -37,6 +37,8 @@ jobs:
     steps:
     - name: Checkout repository
       uses: actions/checkout@v6
+      with:
+        token: ${{ secrets.RELEASE_PAT }}
 
     - name: Fetch and unzip frontend assets
       run: |