iMessages on Mac lost my account phone # and doesn't display it

For the second time in a month, iMessages on the Mac (running Catalina 10.15.7) stopped allowing me to select my phone number in the iMessages Prefs under Account. It shows my email address, but not my phone #. This worked for me properly for years.

It may be related, but like last time this seemed to be triggered by a request from Apple to repeatedly reenter my Apple ID password in just about every place Apple ID is used, on my Mac and my iPhone. When this happened a month ago eventually it stopped asking me and I could use my phone # for iMessage on Mac again, but I don't remember how it happened to start working again.

I did not update software on either my Mac or my iPhone immediately before this happened. I did not change my Apple ID password before this happened.

In my System Preferences : Apple ID preferences, is says that I am "Reachable At" for my phone # for iMessages.

Anybody else have this happen?