sigh Github's idiotic fractal of authentication types.
What upthread is talking about is the Github CLI app, `gh`; it doesn't use a fine-grained tokens, it uses OAuth app tokens. I.e., if you look at fine grain tokens (Setting → Developer settings → Personal access tokens → Fine-grained token), you will not see anything corresponding to `gh` there, as it does not use that form of authentication. It is under Settings → Applications → Authorized OAuth Apps as "Github CLI".
I just ran through the login sequence to double-check, but the permissions you grant it are not configurable during the login sequence, and it requests an all-encompassing token, as the upthread suggests.
Another way to come at this is to look at the token itself: gh's token is prefixed with `gho_` (the prefix for such OAuth apps), and fine-grained tokens are prefixed with `github_pat_` (sic)¹
¹(PATs are prefixed with `ghp_`, though I guess fine-grained tokens are also sometimes called fine-grain PATs… so, maybe the prefix is sensible.)
I’m paranoid but I never authenticate the GitHub CLI - there should be no tokens lying around on my system. If needed, I have some scoped PATs in pass, which I can source as env variables. Git Pushes happen over SSH with Yubikey.