Android has a device-wide backup feature and data-transfer tools for switching phones, but this app's notes are not included in them.
To carry over this app's data, use the app's own "Google Drive Backup". It backs up only this app's data to your own Google Drive, and it's free.
Because you create the backup yourself, it's also useful if you like to back up often or want to move your data to another device such as a tablet. We recommend backing up regularly in case your device is lost or breaks.