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The fix for this problem also fixed an iCloud account problem I've been having for many years. I could not log in to an old non-email Apple ID which had been used to buy many of my apps. I had a permanent red "1" badge on the Settings icon on my phone.

It started when I got a new iPhone 13 mini, and used iCloud restore to get the phone set up quickly. I had bought A LOT of apps under my old Apple ID account, which I'll call fabcdefg. At some point a few years ago, I was prompted to convert that account from fabcdefg to an email address which I'll call fabcdefg@gmail.com. When the restore was completed, it asked me to log in to my fabcdefg account, NOT the converted fabcdefg@gmail.com account. When I typed the correct password, it gave me an error saying that it could not log me in. Today, after reading that the iCloud outage was resolved, I went back to my Apple ID settings and tried again to log in to my "missing" extra Apple ID. Now, instead of asking me to log in to fabcdefg, instead it's asking me to log in to fabcdefg@gmail.com. And it worked!!! So I guess whatever they did either cleaned up some old Apple IDs, or perhaps instead now automatically lets iPhones log in to old non-email accounts using the email address rather than the old non-email userid.
 
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