Pick up organization name in GitHub multi-branch job

### What feature do you want to see added?

After https://github.com/jenkinsci/github-branch-source-plugin/pull/527 , Jenkins can use GitHub app credential without organization settings, automatically picking up organization name inside repo.
But this is currently not supported in GitHub checks plugin.

I tried to implement it in https://github.com/jenkinsci/github-checks-plugin/pull/324 but failed, if anyone has similar need , you may pick up the pr and continue the work.

### Upstream changes

_No response_