Apple really dropped the ball on this issue. I was assigned to a senior support specialist. We spoke on the phone a couple of times and then continued via email. And, then, he ghosted me. No further communication. I sent a couple of follow-up messages, but never received a reply. I find this to be both disrespectful and unprofessional.
So, I proceeded on my own.
First try was to install the OS on an external SSD and set up a minimal account including my AppleID and iCloud info. I was able to send iCloud email from that account.
Then I used Migration Assistant to migrate the original account on the MBA boot drive to replace the minimal account on the external drive. I was not able to send iCloud email from that account.
So, I did what I always resist doing and have done only a few times since becoming a Mac user in 1984: Wipe the internal boot drive and reinstall the OS. This time I migrated from an account I have on my wife's M1 iMac.
That worked. Of course, it was a huge and continuing hassle. The account on the iMac was little used and had almost none of the work I had done on the M1 MBA. Fortunately, I have a recent Time Machine backup of the MBA so I am able to recover things like shell scripts, launchd plist files, etc.
I hesitate to call this a success. Wiping and reinstalling is more a surrender than a solution. It's a lot of work from which you learn nothing.
Oh, wait, I did learn something: Apple can't be relied on to solve difficult problems, even if you still have AppleCare.