I am thinking this was an artifact of the abrupt shutdown of the on-premise server due to the power outage.
After I posted the original message here I remoted into the server machine and killed the Avast service and rebooted the server. I also closed the Avast console browser tab on the workstation I had been using to access the console before I posted the message. When the server came back up I ran the console application and found, in "Notifications", relevant to "Network", the message "Avast antivirus application is outdated" with an "update" link. I clicked that link and the console displayed, almost instantly, a message that the application was updated. (This did not change the version of the On Premise Console; it's still stuck at 6.0.14. So I don't know what, exactly, was updated.) However, after that I was able to look at devices, including the QMS device, without getting a message about an update mirror.
Any thoughts on why the system behaved this way after an abrupt unplanned shut down?