Authenticaton warning when using application default credentials

TL;DR

I'm running a self-hosted GitHub Actions runner on a GKE cluster. Permissions are handled through application default credentials (Workload Identity) and my workflow works correctly (no authorization errors). Unfortunately setup-gcloud still spits out a warning: **Warning**: No authentication found for gcloud, authenticate with google-github-actions/auth.

Expected behavior

I did not expect a warning, considering that the workflow works correctly and interacts with multiple GCP services for which authorization is definitely required.

Observed behavior

An authentication warning is displayed in the workflow logs and as an annotation under the job overview.

Action YAML

name: CICD Bumpversion master
on: 
  push:
    branches:
      - master
    paths:
      - cicd-bumpversion/**
      - .github/workflows/cicd-bumpversion-master.yaml
jobs:
  build-image:
    name: Build and push image
    runs-on: [self-hosted, **REDACTED**]
    steps:
      - name: Set up Cloud SDK
        uses: google-github-actions/[email protected]
      - name: Checkout
        uses: actions/[email protected]
      - name: Build Docker image
        run: docker build -t **REDACTED**/cicd-bumpversion:latest .
        working-directory: cicd-bumpversion/
      - name: Push image to Container Registry
        run: |
          gcloud auth configure-docker
          docker push **REDACTED**/cicd-bumpversion:latest

Log output

No response

Additional information

No response