I think git objects are for a different hosting system than we have here. Git is for working the files. Nostr is for sending the notes about them.
I think you're right on the money with putting the social side on Nostr being the best use.
However, git data itself is just text about the history of the repo. Commits over time. what the parents are, what I've changed. The data itself is also all text, or encoded data into text. Use of it is doing some work in a text editor and then recording that in git as checkpoint in time.
It seems to me you could export to a series of notes and also rebuild a git repo from these notes if they were all on the relay, to be found and parsed.