Our devs built Copycat when creating our (LiveChat's) docs and then they decided to share it with the world. You can use it not only for synchronizing projects between repositories but also for sharing code between multiple projects or connecting a monorepo to a project’s own repository. Enjoy!
To be honest, I would use package for this kind of situation. For example, in Ruby on Rails one could simply create gem and add it to two different repositories. Additional thing is that you have a version control. Nice work anyway!