Mac studio refuse to update the password

You are on the wrong screen. You changed your Apple Account password, NOT your admin login password.

Where you should be is...

System Settings->Users & Groups->click on your admin user account info button ⌽ and change your login password. You will need to enter your current login password to do so.

As has been pointed out your Apple Account password and your user login password are two different things. If you know your current login password (you say you do) you do not need to use the link provided by another user. That only applies if you have forgotten your current password.

Andreas1973 wrote:

[...]

That was what I assumed at first when I went into settings / Apple Account / Sing-In & Security / Password that it is the password for the Mac I am changing, but it only change password on other devices.

That for the Apple Account password that any of your devices would use to sign in to your Apple Account.

Not for signing into the Mac as a user.

So I have looked for any other place to change the password on the Mac but found none. So I assumed it is the same. Make sense to me that the password for the computer is changed in settings for the computer. Right?

The Mac login password is not changed in Settings > Apple Account, but in Settings > Users & Groups.

If you forgot your Mac login password - Apple Support

<< I got a prompt on my iphone to enter the new password. I did and it worked on the iphone. >>

Stop and take a step back for a moment.

You may be confusing your Mac login password with your Apple-ID account password.

• Your Mac login password never leaves your Mac, so it can not be updated or affirmed on your phone.

• Your Apple-ID account only exists on the cloud, so it can not be used at all unless you have an internet connection.

Sometimes the UI does not always work. You can start up in recovery, open terminal and type in resetpassword and follow the prompts. The other way which I have not tried is to boot up your Mac and at the login screen type an incorrect PW 3 times and then when asked you can change your PW.

From recovery you can reinstall the OS and your files.settings should remain in place, however once in recovery then selecting options it should give you a menu of various choices. One is to reinstall the OS. Not sure that would fix your issue but I have done that many times to resolve other issues so may be worth a try.