Hub: Access token for organization i.e. how to authenticate against an organization repository

I am one of the owners of a Docker Hub organization. We want to start pushing images built on GitHub to one of our repositories on Docker Hub.

The question: how to authenticate?

Of course, we could store the personal access token of one of the org owners as a GitHub secret but that would be totally weird. However, there doesn’t seem to be an option to create an org token or similar.

Confirmed by Docker support that this is currently not possible. Follow-up request: Hub: allow access tokens for organizations · Issue #461 · docker/roadmap · GitHub