It looks like gitea supports running a proc_receive hook which can be used to implement pull requests over git:// using a client like
https://git-repo.info/en/(full disclosure) I had written a proof of concept implementation that allows you to use the git-repo.info client to send PRs over git protocol, which you can find here https://github.com/pullreqr/pullreqr_githook
The primary impediment seems partially to be social/coordination where distributed git requires clients to be set up apriori, but it does work in cases where you are using it in house, etc.
I'd kind of be happy to spend more time on it, but with no one actually running the protocol publicly, there is no one to send/receive PRs to or from.