In an app with no user authentication, data is stored in a sqlite db or AsyncStorage on their device. But, some users still want to sync their data between devices. With no authentication flow, data is not uploaded to a database or anything of the sort, so it is not able to be retrieved by multiple devices. In iOS, you are able to use iCloud to sync data between devices that are logged into the same iCloud account. As of now, expo does not support iCloud sync.
react-native-icloud-sync
seems to do just this, but in order to use iCloud sync you would have to eject from Expo as it requires native module linking.
Note* The library does not seem to be maintained, so a new library may be the way to go.