Why all of sudden am I seeing "Verify Email Address Your Apple ID email address must be verified before you can sign in. Verify the address below or choose a different address to use as your Apple ID" when I try to log in to icloud

I entered a different email address, verified that one, then changed my apple id back to the email address I like using. Changing back sent the verification email to that email address like it should have been doing originally 😉

Lot's of folks are getting messages about updating passwords and such. It seems Apple has been tightening up security. I had to update my Apple ID and then I got messages every time I logged in on other devices to do the same. Went on for weeks, so the system is less than ideal. Just this morning iCloud was asking for authentication again. Unfortunately there's little you can do. If you have an alternate email address, log into iCloud with that. If that doesn't work call Apple Support and let them walk you through it.

Contact - Official Apple Support

Yes, I was caught in one of those loops too.