As for the database that handles your business logic … 3 minutes of googling would show that rsync is a poor (or at least a brittle) substitute for multi-master replication when it comes to database engines like InnoDB for MySQL (which is what most websites on the Internet use):
https://dba.stackexchange.com/questions/91287/is-possible-to...
However, you can consider setting up multi-master replication, or if you want your app to be portable, you can set up a replication layer in the app itself. The order of operations should only matter “per activity” (eg chatroom, document etc) and not globally.
That’s what we set up at https://qbix.com/platform — except that the instances don’t all have to be under the control of one company. It’s basically a decentralized social networking platform. Federated, like Mastodon, but far more general-purpose, so you can build any applicatiom with it