push credentials on github actions

👋 Hey!
First, thank you for this wonderful project.
I'm writing here because I'm trying to write a git extension called git-metrics which would allow to store metrics regarding the project, inside git notes, with a simple CLI, so that we don't need to rely on external services.
I have some commands working (add, remove, show) but when it comes to push and pull, it becomes a bit more tricky considering it involves some authentication.
In this PR, I'm trying to use git-metrics push to push my notes, directly from a github action. Using git, we just need to do git push origin refs/notes/metrics and the authentication works out of the box.
With git2, the authentication doesn't seem to work.
Does anyone know, what is the proper way to authenticate using git2 on github actions?
Thank you

Start with the git-metrics push command in the linked PR and trace how it invokes git2 authentication within GitHub Actions. The issue names no repository files or tests; done means establishing a supported authentication path or clearly documenting that path for pushing git notes.