Weirdly enough (or perhaps not, now that the two systems are distinct) I have had zero problems with Scrivener sync on the new iPadOS. It is only the iPhone’s iOS 13.1 that breaks sync. Since others have posted on this thread I want to add that piece of information. Now, off to the discussion thread Amber referred us to.
David, elsewhere it was suggested that maybe (maybe!) it is a problem only on newer devices. For me that is the case. My iPhone SE is a couple of years old and has no problems with syncing on iOS 13. My iPad Mini 5 is brand new and did sync on iOS 12 but not on the new iPadOS. Is your iPad older and your iPhone newer?