How do you find the recovery key to reset your password?

If your Mac is asking for a “Recovery Key” it might well be looking for the FileVault (whole disk encryption system) Recovery Key.

This key was displayed to the “setting-up”

user on-screen during the initial computer setup.

Hopefully it was recorded and securely stored somewhere … and where it is still accessible. 🤞

Volume encryption with FileVault in macOS - Apple Support

If you are talking about the Recovery Key on your account, then review the information here.

Set up a recovery key for your Apple Account - Apple Support

Note, this important message:

This gives you more control of your account recovery methods and can help prevent an attacker from gaining access to and taking control of your account. However, if you lose your recovery key and can’t access one of your trusted devices, you’ll be locked out of your account permanently.

You would definitely want to write down the 28 character code that was given to you when it was set up. If you did not write it down, the only possible way to get the code is by generating another one from a Trusted Device. It is an optional method to increase account security where not even Apple can provide that code for you and Account Recovery is disabled.