Doesn't that only work for single user setups, since a `git push` run from some else's machine could concurrently modify that repo.git directory?

The manual bare repo setup obviously offers no user access management beyond what the system's SSH configuration provides. Beyond that, a bare repository is actually an essential Git feature and what software like Gitea and even GitHub uses behind the scenes.

Given all users can share a user account on a server, it will behave exactly like you expect it to. Again, that's a core Git feature. Additionally, AFAIK Git has its own locking management. Also look up the `--shared` flag. `man git-init` is very helpful.