docs: Use a dedicated API key for docs agents

Co-authored-by: Xuan Yang <xygoogle@google.com>
PiperOrigin-RevId: 883246168

Author: xuanyang15

.github/workflows/analyze-releases-for-adk-docs-updates.yml

@@ -36,7 +36,7 @@ jobs:
       - name: Run Analyzing Script
         env:
           GITHUB_TOKEN: ${{ secrets.ADK_TRIAGE_AGENT }}
-          GOOGLE_API_KEY: ${{ secrets.GOOGLE_API_KEY }}
+          GOOGLE_API_KEY: ${{ secrets.GOOGLE_API_KEY_FOR_DOCS_AGENTS }}
           GOOGLE_GENAI_USE_VERTEXAI: 0
           DOC_OWNER: 'google'
           CODE_OWNER: 'google'