How can I set up a git mirror?

So I've got a RasPi 3B+ and self hosting a bunch of bare Git repos (git init --bare). And I currently store my dots there. BUT I also have a public mirror on Codeberg. For now I just have two remotes set up and do `git push´ individually for each one. And I don't really envision a case where I start developing it on 2 different machines well. I don't know whether those 2 repos are in sync when I'm developing.

Now, is there a more robust way to keep those 2 mirrors in sync?

I was thinking of adding some kind of hook on the Pi, so that I push my changes to the Pi, and then the Pi pushes the same changes to Codeberg. so instead of my current workflow:

home computer -> Pi

home computer -> Codeberg

this happens:
home computer -> Pi -> Codeberg

Is that the right way of doing this?

Please let me know if you have any suggestions!