Rest assured. This app never sends the contents of your notes anywhere and never stores your data on our servers. Your data is stored only on your device.
Only when you use "Google Drive Backup" is data sent to and received from the Google Drive of your own Google Account.
To help us improve the app, there is a setting that shares usage data about this app with the developer (all of it anonymous; it does not include the contents of your notes). To stop sharing, open the menu (≡) at the top left of the Notes screen → "App Information" → "Analysis and Improvement" and turn off "Share Analytics Data".