When you run out of storage space on iCloud, your Notability edits stop syncing to it. This means your notes will no longer sync across devices.
More importantly, your notes are at risk of being lost if you change your device's iCloud access. Since your notes aren't making it off your device, the only place they're stored is in the local iCloud space. If something changes your device's access to iCloud, Apple will clear or remove Notability's access to that space. When that happens, Notability loses access to notes that never made it to iCloud, and they're lost.
Actions to avoid
Do not sign out of your Apple Account.
Do not delete Notability data directly from iCloud without a backup of the note. If deleting Notability notes to create space, make sure the notes are backed up in Notability's native .note format.
Three ways to fix syncing
Turn off iCloud syncing in Notability Settings > Connected Services > iCloud Syncing. This is in Notability, not your device's Settings app.