Remote git server

You can run a git server without any fancy GUI like gitea, gitlab, github, etc. You'll lose the fancy stuff like issues, merge requests, CI/CD and stuff, but you'll have no performance impact on your server what so ever.

Backup

You back it up like any other server, just mirror the files; git stores its metadata in files like anything else. If you move the repository to a new machine, you need to change your local repository's origin to point to it. In .git/config you'll find something like:

[remote "origin"]
url = SOMETHING