It would be fantastic if Gitea were its own OAuth2 provider! In fact, IndieAuth is the perfect candidate for how to implement this.
IndieAuth is an OAuth 2.0 extension, which avoids the centralized problems with existing OAuth solutions by using DNS for "registration" of client IDs and user IDs. Every user account is identified by a URL (for Gitea this could be your Gitea user page), and client IDs are also URLs (would be the Gitea instance home page in this case.)
This would let people sign in to other Gitea instances without any sort of prior relationship or doing client registration and such. Happy to walk through this in more detail if you're interested!