What we really need is federated authentication, but that doesn't exist yet.
This sounds like a great use case for IndieAuth. w3.org/TR/indieauth
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.)
To log in to your Gitea instance, I would enter my own Gitea profile URL. Your instance would then do discovery on my URL to find where to send me to authorize the login on my own OAuth server (my Gitea server), which would then send me back to your Gitea where it would be able to verify the authorization code against my Gitea instance.
I'd be happy to walk through this in more detail if you're interested!