iPhone stuck in Apple ID sign-in loop

After having problems with a Keychain on my Mac, all my iOS devices needed to relog in to my Apple ID.

But my iPhone 12 Mini won't do it: it asks for the PW, I enter it, then it tells me ‘there was an error connecting to the Apple ID server’. I've tried this about 30 times in the last 24 hours. My wife has the same phone, and the same thing happened, but Apple ID accepted the PW first time

Worse still I can not use wifi – the wifi is shown as working, but the device won't connect to the internet (at home or anywhere else). My wife's wife was unaffected

Anyone know what's going on – and how to fix it?

[Image Edited by Moderator to Remove Personal Information]