Still having the very same problem since Catalina. We're on 15.3 already and this issue STILL persists.
I've also changed my password (after a couple of rounds re-doing the validation) and also as directed by Apple Support logged out with my account from ALL devices (MacBook, iPhone, AppleTVs) until the AppleID shows no connected devices anymore.
Still - today (two days after that exercise) I'm back in the same verifcation loop!
But it seems that contrary to others here, after I enter my AppleID PW, MacPW and Iphone Code, the message goes away and also KeyChain is checked (or can be activated). So it all works for me until after 2 or 3 days it's back to the same message. Also I have no problem on iPhone or other devices, just Catalina.
I had 2FA active with my AppleID since years... so it's definitively an macOS Catalina problem.
How on earth is nobody at Apple looking at this and fix it???