I probably should have mentioned this in my original post (will amend) but does it handle things like feature/merge requests kind of like how GitHub and GitLab does?
No, it's just a client, merge requests aren't part of a standard Git install so it wouldn't know where to even save them. (It does handle them when working with a Github repository).
For that Gitlab is certainly the best option – or a private repository at Github. I'd trust their security much more than anything I could roll myself.