Gcloud auth login inside playbook

Hi All,
I am trying to run a ansible playbook inside a github workflows, the playbook needs cloud sql proxy to connect to private google cloud sql instance. Below is the snippet of my github workflows pipeline:

name: Ansible Shared CI/CD pipeline DEV

on:
workflow_call:
inputs:
DB_NAME:
required: true
type: string
DB_INSTANCE_NAME:
required: true
type: string
DB_HOST:
required: true
type: string
DB_USER:
required: true
type: string
GCP_PROJECT:
required: true
type: string
SCRIPT_PATH:
required: true
type: string
DB_INSTANCE_LOCATION:
required: true
type: string

env:
DB_INSTANCE_NAME: ${{ inputs.DB_INSTANCE_NAME }}
DB_NAME: ${{ inputs.DB_NAME }}
DB_HOST: ${{ inputs.DB_HOST }}
DB_USER: ${{ inputs.DB_USER }}
DB_PASSWORD: ${{ secrets.DB_PASSWORD }}
GCP_PROJECT: ${{ inputs.GCP_PROJECT }}
TOKEN_KEY: ${{ secrets.GH_PAT }}
SCRIPT_PATH: ${{ inputs.SCRIPT_PATH }}
DB_INSTANCE_LOCATION: ${{ inputs.DB_INSTANCE_LOCATION }}
WORKLOAD_IDENTITY_PROVIDER: ${{ vars.DEV_WORKLOAD_IDENTITY_PROVIDER }}
SERVICE_ACCOUNT: ${{ vars.DEV_SERVICE_ACCOUNT }}
TF_TOKEN_app_terraform_io: ${{ secrets.TF_API_TOKEN }}

jobs:
data-prep:
permissions:
contents: ‘read’
id-token: ‘write’
runs-on: ubuntu-latest
if: always()
steps:
- name: Checkout the repo
uses: actions/checkout@v3

  - id: 'auth'
    uses: 'google-github-actions/auth@v1'
    with:
      token_format: 'access_token'
      workload_identity_provider: '${{ env.WORKLOAD_IDENTITY_PROVIDER }}'
      service_account: '${{ env.SERVICE_ACCOUNT }}'
      project_id: '${{ env.GCP_PROJECT }}'

  - name: 'Setup Cloud SDK'
    uses: 'google-github-actions/setup-gcloud@v1'

  - name: 'print SA'
    run: | 
      sa_file=$(find . -name "gha-creds*" | awk -F"/" '{print $2}')
      echo $sa_file
      cat $sa_file
      

  - name: 'Create Temporary storage bucket'
    run: |
      gcloud config set project ${{ env.GCP_PROJECT }}
      gcloud storage buckets create gs://${{ github.sha }} 

  - name: Copy Artifacts to bucket
    run: |
      gsutil -m cp -r . gs://${{ github.sha }}

playbook-execution:
needs: [“data-prep”]
permissions:
contents: ‘read’
id-token: ‘write’
runs-on: ubuntu-latest
if: always()
steps:
- name: Checkout the repo
uses: actions/checkout@v3
with:
repository: brtspd/ansible-repo
ref: refs/heads/master
token: ${{ env.TOKEN_KEY }}

  - id: 'auth'
    uses: 'google-github-actions/auth@v1'
    with:
      token_format: 'access_token'
      workload_identity_provider: '${{ env.WORKLOAD_IDENTITY_PROVIDER }}'
      service_account: '${{ env.SERVICE_ACCOUNT }}'
      project_id: '${{ env.GCP_PROJECT }}'

  - name: 'Setup Cloud SDK'
    uses: 'google-github-actions/setup-gcloud@v1'


  - name: Download artifacts from bucket
    run: |
      gcloud config set project ${{ env.GCP_PROJECT }}
      gsutil -m cp -r gs://${{ github.sha }}/* .


  - name: List files
    run: |
      ls -lrt

  - name: 'Setup Ansible'
    run: |
      sudo apt update
      sudo apt install -y software-properties-common
      sudo add-apt-repository --yes --update ppa:ansible/ansible
      sudo apt install -y ansible

  - name: 'Which python'
    run: |
      which python3
      which ansible-playbook
      ansible-playbook --version

  - name: 'Setup Ansible collection'
    run: |
      ansible-galaxy collection install community.postgresql

  - name: 'Check if proxy is running'
    run: |
      ps -ef | grep "proxy" | head

  - name: 'Run ansible playbook'
    run: |
      ansible-playbook postgres-deployment.yaml -e db_instance_location="${{ env.DB_INSTANCE_LOCATION }}" -e gcp_project="${{ env.GCP_PROJECT }}" -e db_name="${{ env.DB_NAME }}" -e ansible_host="${{ env.DB_HOST }}" -e db_user="${{ env.DB_USER }}" -e db_password="${{ env.DB_PASSWORD }}"

  - name: 'Stop cloudSQL proxy'
    run: |
      pid=$(ps -ef | grep "proxy" | head -1 | awk -F" " '{print $2}')
      sudo kill -9 "$pid"
      exit 0;
      
  - name: Delete storage bucket
    if: always()
    run: |
      gcloud config set project ${{ env.GCP_PROJECT}}
      gcloud storage rm -r gs://${{ github.sha }}

I have authenticated to google cloud platform inside the github workflows but the ansible playbook is not detecting application-default credentials. How do authenticate to GCP inside playbook without making use of service account keys?