There's no such thing as an account with or without login permissions. Normally you need a git account. And that means you can log in to it. And then you have to try and configure your ssh server so that after logging into the git account, you can only run the git server (I forget the command). If a mistake is made with this configuration then you can log in or port forward or X forward or file transfer as git.
This is a terrible idea because it's blacklist-based security. Places like GitHub have their own ssh server that only runs the git server and nothing else.
I suppose /usr/sbin/nologin is not a thing?
https://www.man7.org/linux/man-pages/man8/nologin.8.html
That's a hack. It's a login shell that, once you have already logged in and run the shell, prints a message saying you can't log in or run a shell, and then exits.
It does not stop you from, say, logging in to SSH and then starting a port forward. Or running a command in a way that bypasses the login shell. ssh will always pass it to your login shell but other ways can be vulnerable.
SSH bastions would like a word I guess. You can authenticate, but you definitely can’t login (which is also the case for git over SSH).