There's plenty of git forges that aren't GitHub. Git itself has nothing to do with central servers and can theoretically be used in a completely decentralized manner.
At college some guys were self hosting a git server for a project but it went down. We resorted to a USB stick that acted as remote and was passed around. That was awesome to see, for about a day...
Heck yeah, git is a Swiss army knife for versioning all kinds of things beyond programming repos.
Outside of work, I've been using git in local "working" or "sandbox" directories on my personal machines for ages where I do everything. Just have an alias to quickly stage and commit with simple search tags in the commit message, and only move out copies of documents, spreadsheets, 3d printing projects, video and image edits, songs and tabs, etc. after I get them to their "final" point. It's been a lifesaver for recovering disastrous program crashes that can corrupt files, on more than a few occasions.
Speaking from experience, in the past year, I've used 3 different hosting providers for git repositories at work. Only one of them is GitHub. It's good to keep your options open - git isn't locked to any particular provider, after all.
I've used GitLab and Azure DevOps professionally, but there are a lot of services out there which host Git repositories. GitLab can also be self-hosted which is nice. They all fundamentally work the same though from my experience - code viewer, issue tracker, pull requests, some way of doing CI/CD, and various collaborative and documentation features (wikis, discussion areas, permission management, etc).
It may be good to understand also where the separation lies between features that are part of Git vs those which are part of the service you're using (like GitHub). For example, branches are Git, while pull requests and wikis are GitHub.