Thanks soph2009,
It does sound like you're doing everything correctly to change the Notes password.
Since you're getting an Apple ID password error, and you mentioned earlier that you have "changed my Apple ID password many times", we want to see if you can login separately from Settings > Notes.
Try at the Apple ID log in page:
Apple ID > Tap on Sign In > Enter your Apple ID and password. Are you able to log in successfully?
• If not, you'll need to select Forgot Password, so you can change the Apple ID password: Change your Apple ID password - Apple Support
•If you're able to log in successfully:
- Restart your iPhone: Restart your iPhone - Apple Support
- Go to Settings > Notes
- Password
- Change Password
Let us know what happens.
Take care!