Log out of a locked device to access a new password?

Are you quite certain you contacted Apple? If you found them through a Google search for example be advised that Google is by far and away the greatest disseminator of false or fraudulent "apple support" information. A "password change email" strikes me as a phishing scam.

Anyway, assuming you contacted legitimate Apple support personnel, they would have referred you to their Support document, here: If you forgot your Mac login password - Apple Support. How far did you get with it?

Eventually, the instructions lead to erasing the Mac and restoring its content from a backup, but there are many options to exhaust prior to resorting to that ultimate step. For example, there are many statements that begin with "if you see this" or "if you are asked" for something due to the many Mac models and macOS versions that have evolved over the years. You have to methodically exhaust all of them.

If you are unable to use your Apple Account credentials you would not have been able to log into this website (Apple Support Community). You can use those credentials to unlock a Mac if and when prompted for them.

AndreaFred wrote:

I went through support after being locked out of my MacBook Air. They verified me and sent a password change email.

I have never heard of that procedure with Apple. I am concerned that "they verified me" means "they" obtained personal identifying information about you with that. I have also never heard of Apple sending a "password change email." I can't find anything sounding like that in Apple's online support documentation.