Add GCP Authentication and switch to Vertex AI mode for updater workflow

Author: xuanyang15

.github/workflows/update-python-docs.yaml

@@ -32,6 +32,12 @@ jobs:
         with:
           python-version: '3.11'
 
+      - name: Authenticate to Google Cloud
+        id: auth
+        uses: 'google-github-actions/auth@v2'
+        with:
+          credentials_json: '${{ secrets.ADK_GCP_SA_KEY }}'
+
       - name: Install dependencies
         run: |
           python -m pip install --upgrade pip
@@ -40,7 +46,6 @@ jobs:
       - name: Run ADK docs updater script
         env:
           GITHUB_TOKEN: ${{ secrets.ADK_BOT_GITHUB_TOKEN }}
-          GOOGLE_API_KEY: ${{ secrets.GOOGLE_API_KEY }}
           GOOGLE_CLOUD_PROJECT: ${{ secrets.GOOGLE_CLOUD_PROJECT }}
           GOOGLE_CLOUD_LOCATION: ${{ secrets.GOOGLE_CLOUD_LOCATION }}
           GOOGLE_GENAI_USE_VERTEXAI: 1