How to restore app data from iCloud without restoring iPad from Backup?

I had an iPad which was under remote system management from my old school, so when I left I had to reset the iPad to factory settings and not restore from iCloud backup when setting it up again, so that it wouldn't restore the management from my old school again.

However, the apps that I've redownloaded (games and GoodNotes), which had app save data on the iCloud, haven't been restored since it thinks it's a new iPad. Is there a way to transfer the iCloud save data onto this new iPad for specific apps, without restoring the whole iPad to its iCloud backup?