The current version of notebook 6.0.3 doesn't appear to be 100% compatible with Android 13 or maybe Samsung UI 5.
The app runs, but is missing a permission request. It will ask to be granted permission but the app doesn't have the correct request. It needs to grant files / media storage access.
I have two devices, one on Android 13 and one on Android 12. On Android 12, the permission is there and granted.
On Android 13, the permission is not listed in settings of the app.
Sharing files/pictures/etc from the system or another app to notebook works on Android 12, but doesn't on Android 13. You get this message: