Private Notes addon doesn't collect any data.
Further more, this addon doesn't have any host permissions, so it cannot submit any data.

All notes data are stored encrypted within addon itself. Your browser may synchronize these data with your other devices if you use "Firefox Sync.", "Chrome Sync." or similar browser build-in feature.
Password is not stored - it's hashed with PBKDF2 function with 100k iterations and strong salt. This hash is then stored with the notes.
Settings data are stored locally and not synchronized nor encrypted - these are not sensitive data.
Automatic backups are stored locally, encrypted and not synchronized.
Manually exported backups are encrypted - so it's safe to store it anywhere - as long as your password is strong enough (the longer the better!).