Time Machine cannot connect to backup disk
I use Time Machine to backup my MacBook Pro to an external drive connected to a Mac Mini on the same network. This was working fine until I updated the OS on the Mac Mini to Mac OS Monterey. Now, when I try to select the backup disk on the Mac Mini from the Time Machine panel in System Preferences on my MacBook, I get the error "Time Machine can’t connect to backup disk. There was an error authenticating the provided user name and password". If I purposely type in the wrong password, I get the immediate shaky dialog, rejecting the wrong password. It seems that the Mac Mini is accepting the password, but Time Machine is not? Using the exact same user name and password I can easily bring up Screen Sharing on the Mac Mini from the MacBook.
Any idea why my user name and password would be rejected when trying to use Time Machine?
Note: I do have "Share as a Time Machine backup destination" checked in the Sharing Panel for the external drive on the Mac Mini.
And, again, this was all working fine before I updated the Mac Mini to OS Monterey.
Thanks.
MacBook Pro 15″, macOS 10.12