As I've been housebound for some time I had not set two factor authentication on my iphone. Today I received my new Apple watch 10 which insisted I had to have two factor authentication so have set that up. And now icloud keeps giving me that pop up which then prevents me doing anything until I close the two screens, and within 30 seconds it is back.
Kept telling me to sign in to one of my devices for an authentication code, I was already signed in to my phone and unlike when I used my ipad and a code was automatically sent on to my phone, nothing happened.
I've stopped icloud opening at start up on my PC (Windows 11 - all W11 updates have been installed)
I don't use icloud to back up photos or my devices, purely to transfer pdfs such as manuals, tickets, timetables.
I've uninstalled icloud app but this now means I cannot sync any of my pdfs into files to be able to read them on my device (some are too large to attach to an email).
I shall try the recommendation in ronidy's post.