Error "action could not be completed" can't sign in to my Apple ID on iPad

Try using an entirely different WiFi network. Perhaps a friend or cooperative neighbour would allow you to try with their own WiFi connection.

Otherwise, seek assistance from Apple Support or a the Genius Bar at your local Apple Store - as already advised.

You may find that a restart of your WiFi Router, followed by a restart of your iPad will clear the problem - otherwise you may have no alternative other than to restore the iPad using a Mac computer or Windows PC.

To restart your router, disconnect power from the router for at least 30 seconds - then reconnect power to restart. After your router reboots (which may take several minutes), force restart your iPad:

Force restart iPad (models with the Home button)

Press and hold the top button and the Home button at the same time. When the Apple logo appears, release both buttons.

Should it be necessary to escalate your issue to Apple Support, the quickest route to engaging with Apple Support will be via the Support link at top-right or bottom-left of this page - or using this link:

Official Apple Support

You might also visit the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP) - where the technicians will be able to offer assistance:

Genius Bar Reservation and Apple Support Options - Apple

I don't need "to check it out". As a regular contributor here, I'm fully aware of thread that you reference. You can, of course, contribute to the thread yourself with a "me too", not that you will be any further forward.

As you will learn from the thread, Apple are reported to be aware of the broader issue - hence my recommendation, if you are unwilling to attempt self-help using a Mac or PC, that you contact Apple Support for assistance.