The cgit docs indicate that cgit compiles git into itself as well.
Is that git version used by your whole server or is it used internally by cgit only to parse the git repositories?
The git version is statically compiled into cgit, it is independent from the server. In fact, cgit can run without having git installed (it does not execute an external program).
For example, consider the cgit package in Arch Linux, git is not marked as dependency. There is a single binary resulting from the build process.