I am also facing this issue but I am not doing it from organisation(its from my personal profile) So, let me explain you what I did to solve this

name: "Build Docker Registry"
       runs-on: ubuntu-22.04
       permissions:
          contents: read
          packages: write
       steps:
        - name: Checkout 
          uses: actions/checkout@v4
        - name: Login to Docker Hub
          uses: docker/login-action@v3
          with:
            username: ${{ github.repository_owner }}
            password: ${{ secrets.GITHUB_TOKEN }}
            registry: ghcr.io
        - name: Build and push
          uses: docker/build-push-action@v2
          with:
            context: .
            file: ${{ env.DOCKERFILE_PATH }}
            push: true
            tags: |
              ghcr.io/${{ github.repository_owner }}/${{ env.DOCKER_IMAGE_NAME }}:${{ github.sha }}

Do it this also,

So, see here is my package

you can see the full .yaml file here - https://github.com/manzil-infinity180/dumpStore_backend/blob/main/.github/workflows/ci.yaml