I use https://fedoraproject.org/coreos/ for my server/website. My host doesn’t offer it as an image so I have to upload it myself, but I use an ISO I made with the CLI to automatically set up everything anyway. It works pretty well, I configured auto updates and I can just forget about it.
You missed out this fairly important bit re go-git:
it is not supported or packaged because it is not fully compatible and could corrupt Git repositories.
As far as being tied to git proper, that’s because there is no drop-in alternative implementation that implements all the functionality that you need to run a Git server. Right now, Git proper is your only option. That might change as gitoxide matures, but that could take years.
Not right now.