Can authenticate to network machine for Time Machine backup

I just replaced a Mac mini 2014 with a new machine. I used Migration Assistant to copy over everything to the new machine. I plugged the old external drive I was using for backups into the new machine. When I tried to do a Time Machine backup from a Macbook Pro on the network, which I have been doing for years, I get the message 'Time Machine can't connect to the backup disk. There was an error authenticating with the provided username or password.' This also happens with another Macbook Pro on the same network. All machine are running Monterey 12.2.

I've tried several suggestions found by a web search, but nothing works. I've just now reformatted the drive, recreated the container, recreated the volumes (with different names), and reattached the drive. Time Machine works on the host machine (the Mac mini) but I still can't access the backup volumes remotely from either Macbook Pro, even though the volumes are shared, with proper permissions, as Time Machine backup volumes.