Are you using Faster Docker Volumes?
I wrote out instructions on how to sync with Dropbox here: Using Local on multiple computers
As long as the domain is the same, there’s no reason why the Local site manifest needs to be synced.
Syncing MySQL with Dropbox is less than ideal due to conflicts that are bound to happen—even with other products like MAMP.
We totally understand the need for syncing sites. It’s something we plan on incorporating into Local Pro.