Proper Container Registry Procedure

I noticed here: Package Registry | Gitea Documentation
that packages always belong to an owner, not a repository.

I have used the following action:

- name: Login to GitHub Container Registry
  uses: docker/login-action@v3
  with:
    registry: GITEA_URL_GOES_HERE
    username: ${{ github.actor }}
    password: ${{ secrets.GITHUB_TOKEN }}

The login is successful, however, when I try to push an image, the following error occurs:

unauthorized: reqPackageAccess

If I replace the password line with a personal access token, the docker push succeeds, but it goes to the owner’s packages.

From the link I included above, there is this:

To link an (already uploaded) package to a repository, open the settings page on that package and choose a repository to link this package to.

That is a very manual process. Is there a way to automatically link a package from an owner to a repository?