Forgot password for old locked notes. Need help resetting or recovering them

Your ONLY option is to remember and enter the password.

There is no other recovery process or workaround.

There is nothing that anyone else or Apple can do to help.

Sorry.

The “good news” is that there’s no limit on “failed attempts” … so just keep on trying.

Excerpt from Apple article on the matter.

“… Don't forget your Notes password. Apple doesn't have access to locked notes and can’t help you access them if you forget your password …”

Ref: How to lock or unlock notes on your iPhone, iPad, and iPod touch - Apple Support

FWIW, it appears that this is being updated in iOS 16 so as to be tied to your existing device and/or AppleID credentials.

“ … Lock a note using just your device passcode, eliminating the need to remember a separate password …”

Presumably, this would allow locked-notes recovery if the proper identifying credentials are provided.

Doubtful that this would (or even be technically possible) retro-actively to already-locked notes though.

Ref: iOS 16 Preview - Apple