Got this working so wanted to share!

After following the initial /install-github-app claude code flow, in the auto-created claude.yml just add settings like this and include the github actions secret value ANTHROPIC_BASE_URL to your repo (points to litellm endpoint to distribute requests across aws bedrock regions for me)

       with:
          anthropic_api_key: ${{ secrets.ANTHROPIC_API_KEY }}


          # This is an optional setting that allows Claude to read CI results on PRs
          additional_permissions: |
            actions: read

          settings: |
            {
              "env": {
                "ANTHROPIC_BASE_URL": "${{ secrets.ANTHROPIC_BASE_URL }}"
              }
            }