Edit: I do like how neat it sounds to just query a user's public Gists though.
I've actually been thinking about different ways of adding exactly that to a static site - technically you could have something like a comments form that just writes to a text file somewhere (perhaps updating a Gist with the API you mentioned[1]), which the static site reads from upon page reload.
Sounds a bit inelegant I guess, but could be interesting to implement.
[1] https://docs.github.com/en/rest/gists/gists#update-a-gist
Alternatively there's https://github.com/giscus/giscus, which instead uses github discussions.
Haven't used either so can't comment (heh) on their "performance".