from iOS (iTunes)
You can back up notes from iOS devices via Windows or macOS (earlier than Catalina):
Download iTunes from https://www.apple.com/uk/itunes/
Connect your device to your desktop computer
Launch iTunes on your desktop computer
Select your connected device on the left panel of iTunes
Select "File Sharing"
Select "Unique Bible App"
From document window, you should see a file "Notes.sqlite", which contains bible notes.
Back up this file as you like.
For more instructions on using file sharing feature via iTunes, please read https://support.apple.com/en-gb/HT201301.