I have no idea what everyone is on about.
Host your own git repo. It’s trivial and built into git and you make every decision about it from the ground up.
For example you don’t need to worry about registrations or what country it’s hosted in because the country it’s hosted in is your hard drive (or your company’s server rack).
Then use whatever front-end you want and point it at that private repo.
It’s only mildly more fiddly to set up and grant access, but it sure doesn’t ask you for a credit card and it sure doesn’t get scraped to train LLMs (unless you make it internet-facing and don’t protect it).
If you want to stay close to the core experience but still have a decent interface, check out (heh) gitweb and git daemon. Though I wouldn’t mind if gitweb had some of the fancier features, like the “download as zip”/“git clone path/to/branch copy-to-clipboard” buttons.