There is a lot in this thread.. I hesitate to get into these longer threads where people are expressing frustration/irritation.
I chose a random person to respond to, so don't bite my head off for choosing to comment or who I 'replied' to. All I am hoping to do is help one or two of ya.
If none of this helps, I'm sorry.. it's all I know, and you'll have to rely on contacting Apple support.
If you're not aware, this is a user to user forum and Apple is not here. So if you are waiting for Apple to directly respond and address questions/issues in this thread, they will not.
First of all, this is the best link to reference for locked notes..
How to lock or unlock notes on your iPhone, iPad, and iPod touch - Apple Support
This link has a section on it for how to reset your notes password.
I can't speak to those of you who insist that you're entering the correct password.
I also don't work for Apple and cannot speak to whether or not there could be a bug or something affecting you.
But maybe I CAN clarify something that may not be clear to you..
If you go thru the process of resetting your notes password, that does not unlock your prior notes. It resets the password for all notes that you may lock in the future.
SO, if you reset your notes password, and then enter your new password into an older locked note and insist that you are entering the correct password, you are not entering the correct password that the note was locked with. A note can only be unlocked with the password that was used to lock it.
As Apple has told some of you, the only way to lock a note is using a password.
Without having first set a password for locked notes, the option to use FaceID to unlock them will not even be available.
FaceID is available to make something more convenient. It does not (and will not likely ever) replace your password.
I don't know what all the triggers are, but there are things that will require the notes password to be re-entered in order to re-enable unlocking your notes using biometric method.
Similarly, you might use Face/TouchID to unlock your iPhone.. the only way to do that is if you have a passcode set. If you forget the iPhone passcode when it's requested, you're hosed and you'd have to restore your iPhone, hopefully you were backing it up.. Because Face/TouchID is not a replacement for the passcode. It is a convenience.
Apple cannot 'remotely' unlock your notes or reset a password for a locked note. the password set to lock your notes is the encryption key.. stored locally on your device (I think).
You should have unlimited guesses for the locked notes password, so try any common passwords you may have used. After an incorrect guess or two, IF you entered a password hint at the time of password creation, it should be displayed.
Keep in mind that when you created this password for your locked notes, it may have been years back and on a different device. I update my phone annually as part of the iPhone Upgrade Program.. and when I transfer to the new phone, I do not believe I have to re-enter the password for my locked notes. I just set up Face ID and I'm off and running.