Migrations refers to changes in the database structure. You’re not talking about pushing source code changes, which is what git is for.
Changing mail templates, and key much everything else not involving a custom plugin is done via the web interface and can’t really hurt anything, so it’s not the kind of thing that many people feel the need to do on a staging server.
If you were to develop a custom plugin that needed testing you’d host it in github and test it on a development or staging server and then rebuild to pull in the new code from git.
It sounds like you’re not planning to do that.