Why does my Apple Watch setup fail with Two-Factor Authentication?

Setting up a new Apple watch fails with this message:

"Setting Up Apple Watch Cannot be Set Up

This feature requires two-factor authentication. The Apple Account 'XXXX

@macom' does not support two-factor authentication."

I have been attempting to set up an apple watch (series 6, pairing with iPhone 13 mini). It has previously successfully paired and set up using my iPhone 13 and ID (therefore not a hardware incompatability), but now am setting up fresh for my dad. He has had two factor authentication enabled on his ID for years, but each time apple watch setup fails with the message above.

The Apple watch is removed from my account so should be free to use on his account. I've tried restarting both devices. Every attempt fails with this message. Recently set up his iPhone 13 mini and iPad Pro on this same account without any two factor authentication issues.

[Re-Titled by Moderator]