Backing up my repositories to self-hosted Gitea

I’ve been gradually moving more of my setup to self-hosted services. After turning my old ThinkPad into a home server, one of the next logical step was to back up all my Git repositories.
Most of my projects live on GitHub, and other places I use for contract work.
For a while, I just ran an rsync backup of my local clones. It worked, but it wasn’t a real solution — no metadata, no browsing, and no way to restore easily.