I have never used this tool but Google open-sourced Copybara[1]. If you look at the commits of their other open-source repositories, it seems this tool is often used.
Looks a bit heavy though for my liking but maybe they have some good ideas.
> Copybara requires you to choose one of the repositories to be the authoritative repository
Looks like it is more angled at mirroring private to public.
I've seen Copybara used at Google in both directions: for some projects, the internal repo is the authoritative one, and for others, the external repo is authoritative.
Copybara is not prescriptive, you can go in either direction.