Verify GitHub access

The final GitHub verification has two distinct parts: gh_auth proves that the PAT can log gh in, while gh_repo_access proves that the authenticated identity can access the actual repository. A successful login alone is not sufficient.

echo "$GITHUB_PAT_TOKEN" | gh auth login --with-token && gh auth status

The statuscheck also checks repository access. A fine-grained PAT must be scoped to the repository you are actually configuring; Contents and Pull requests must both be read/write.