Backing up data manually might fail in some cases with an "OZZipException" or "ZIPFoundation" message like this:
This means that the app can't create a .zip file containing all your documents, most likely because you're running out of device storage. Please verify this by going to your device Settings > General > iPad / iPhone Storage, and if the device storage is in fact low, please follow the recommendations to free up more space and retry the backup process.
Tip: A quick way to free up space is to offload the app, which will clear its temporary storage but keep your documents intact. On the same iPad/iPhone Storage page in device Settings, continue to GoodNotes > Offload App. This might take a while. After that, tap "Reinstall App" to have all your documents placed back.