How to deploy flutter to firebase through github actions using workload identity federation

When deploying flutter to firebase from local machine I do following and it works:

flutter build web
firebase deploy

When trying to deploy from GHA , my yaml file looks like this

test_deploy_to_dev:
    name: deploy
    needs:
      - label_check
    permissions:
      contents: read
      id-token: write

    runs-on: ubuntu-latest
    steps:
      - uses: actions/checkout@v3
      - id: auth
        name: 'Authenticate to Google Cloud'
        uses: 'google-github-actions/auth@v1'
        with:
          workload_identity_provider: 'projects/1111111/locations/global/workloadIdentityPools/abc/providers/xyz'
          service_account: 'firebase-deploy-flutter@project123.iam.gserviceaccount.com'

      - uses: subosito/flutter-action@v2
        with:
          channel: 'stable'
          cache: true
      - name: Run flutter pub get
        run: flutter pub get
      - name: Enable flutter web
        run: flutter config --enable-web
      - name: Build Web App
        run: flutter build web
      - name: deploy flutter to firestore
        run: |
          npm install -g firebase-tools
          firebase init
          firebase deploy

Google auth part works.
In GHA, I get error - Failed to authenticate, have you run firebase login?

Error Failed to authenticate, have you run firebase login? happens because workload identity is not setup correctly.

Dont follow Official doc. It has a small error.

Instead follow Github doc. It shows how to create WIF through CLI and provides a working template to authorize GHA through WIF.

• Enable "Firebase Management API" in your GCP project
• Firebase project and gcp project are 2 different things. I was using sv_account from a gcp project to deploy into a different firebase project. Hence all those auth errors shown below.
• sv_account needs following permissions:
  • Firebase Hosting Admin
  • Service Account User
• In GHA template provided in Github doc link above: in workload_identity_provider key:
  • workload_identity_provider: 'projects/<gcp-project-id>/locations/global/workloadIdentityPools/<my-pool-id>/providers/<provider-id>'
  • use pool_id and provider_id. Dont use pool_name and provider_name
  • gcp_project_id (all int) is different from project_id.