They have translation files in a standard filetype that a translator can work from and just submit via an email to the devs. They will then convert that as necessary to whatever system or syntax their specific project uses.
They will have a translation guide that explains the specific syntax their system uses, with examples, so they can just drop the file in when it is submitted. Also usually submissions via email or something simple anyone can do easily. The file format itself will usually be editable in a standard text editor so any computer can open it without needing any special software.

Requiring a volunteer translator to submit something like that through git is ridiculous. It's exactly the thing a software engineer would so no issue with. The same thought process that says a direct API is all the end users need, a GUI is a waste of time and dev effort. The entire reason front end UX teams are so important.