This kind of stuff takes a nontrivial amount of time and effort to setup and _automate_. Plus at the end of the day you still need to host the repo itself some

This kind of stuff takes a nontrivial amount of time and effort to setup and _automate_. Plus at the end of the day you still need to host the repo itself somewhere (not just the web UI), which means you will need a hosted place you can write to via Git's push mechanisms... It's not impossible but finding free managed hosting for this seems nontrivial too.