GCP - Cloud Run : "Error: The user is forbidden from accessing the bucket"

I am writing a GitHub Action to deploy my application to GCP's "Cloud Run" service.

name: Deploy to production

on:
  push:
    branches:
      - master

env:
  PROJECT_ID: XXX
  SERVICE_NAME: XXX
  RUN_REGION: XXX
  PACKAGE_VERSION : XXX

permissions:
  contents: read
  id-token: write

jobs:
  deployment-job:
    runs-on: ubuntu-latest
    environment: production
    steps:
      - uses: actions/checkout@v2
      - name: Authenticate to Google Cloud
        uses: google-github-actions/auth@v0
        with:
          workload_identity_provider: XXX
          service_account: XXX
      - name: Deploy to Cloud Run
        uses: google-github-actions/deploy-cloudrun@v0
        with:
          service: ${{ env.SERVICE_NAME }}
          source: gcr.io/${{ env.PROJECT_ID }}/${{ env.SERVICE_NAME }}:${{ env.PACKAGE_VERSION }} # equivalent to "gcloud builds submit ..."
          region: ${{ env.RUN_REGION }}
          tag: ${{ env.PACKAGE_VERSION }}

I run into this error :

ERROR: (gcloud.beta.run.deploy) The user is forbidden from accessing the bucket [XXX]. Please check your organization's policy or if the user has the "serviceusage.services.use" permission

I tried to add this permission to my service account but I am still running on the same error :

gcloud projects add-iam-policy-binding XXX --member=serviceAccount:XXX --role=roles/serviceusage.serviceUsageAdmin

I set up the Workload Identity Federation from this tutorial.