why do the verification codes sent to my mac NEVER work

Ok good.

Suggest that “Next Time” try using the verification code self-generated by your laptop to see if it possibly works more consistently.

1. Go to Apple menu  > System Settings, then click your name.
2. Click Sign-In & Security > Two-Factor Authentication.
3. Click Get a Verification Code.

Source:

Get a verification code and sign in with two-factor authentication - Apple Support

If there is STILL a problem w/ consistency; check to ensure that your Mac’s internal clock is accurately set, with the proper time zone, AND is configured to auto-sync with a networked time server.

Change Date & Time settings on Mac – Apple Support (AU)

I don’t understand something.

Are you actually logging-out of your AppleID in your MacBook? (Your post could be interpreted that way)

Normally you just log-out of your Macbook … and back-in … w/ you local user device password and never “mess” w/ your AppleID or 2FA verification codes.

the standard way of logging in to your Mac is with the local username and password created when you first set up your Mac. This does not require an Internet connection or anything to do with your Apple-ID.

if you FORGOT you original password, then as an emergency bypass, you can sometimes log in with your Apple-ID.

This requires an internet connection, and if you have not confirmed anything about your Apple-ID recently AND two-factor authentication is enabled, then you will need to authenticate your Apple-ID using your second factor, often an iPhone or other Apple device.

But that will not log you in, it merely authenticates and validates your Apple-ID. AFTER Authentication, THEN you can use that now valid Apple-ID to attempt to log in to your Mac ON an EMERGENCY basis, provided it also has an Internet connection.

That screenshot raises more questions than it answers … it say’s an iPhone is trying to sign-in … ?

Was this pop-up in direct response to an action initiated by you … from an iPhone ???