iCloud.com won't verify my mac.com email OR let me switch to a me.com/icloud.com alias
In the last few months any time I have tried to log in to iCloud.com I've gotten a message during the login process that says I need to verify the email associated with my AppleID, which is a mac.com address. When I ask to be sent an email so that I can verify it, the system says one is sent, but it never shows up (not in my Inbox, Junk, or any of the other folders I can access on my iPhone). I can't check for it any other way, since I would need to log in to iCloud to check for it, but iCloud says I need to get the email in order to log in.
I know it's not a problem with my AppleID, because when I enter the mac.com email address and my password, I get a two-factor verification number sent to my iPhone. I say to allow the conection and enter the number in iCloud.com, at which point I get a pop-up which says "Your Apple ID email address must be verified before you can sign in."
As I said, if I enter my mac.com address, the system says an email has been sent, but it never shows up. When I tried to enter the @me.com or @iCloud.com aliases, thinking maybe mac.com is no longer supported, I got an error message that says "the application type specified is unacceptable."
It does give the suggestion that I can change my AppleID, which is COMPLETELY UNACCEPTABLE as a solution. The last time Apple forced me to change my AppleID I lost all of my iTunes purchases and their tech support was unable to restore them, even though I spent hours on the phone over the course of two weeks trying to do so. I'm NOT going through that again, so need a solution that allows me to keep my current AppleID.
iPhone XR, iOS 14