I’m also interested in this. I have a similar use case, to implement “cross device sync” functionality for a local-only webapp. I tried out automerge but it felt like it’s meant for syncing data when multiple users collaborate, and not data sync for a single user who is expected to use only one device at a time (I could be wrong about this).

I have implemented a POC sync mechanism via central server and I believe it’s simpler as it takes advantage of certain assumptions about the app. I’ve yet to productionize it so I am interested in knowing if my understanding is correct or if there are other existing solutions for this use case.