For what it's worth, terminating Teams by closing the app window did nothing, (as I think others have reported.) In Task Manager, there was a group of processes under the Apps category, and the problem was ultimately solved by terminating that group.
What may be useful, however, is the observation that, before I deleted that group, I found a lengthy list of Teams processes, most of which were labeled Teams (32-bit) and I'm sorry I didn't keep more accurate notes about this as I was thrashing at the time. I can say that the problem wasn't solved by deleting those extra processes. It continued until after all Teams processes were terminated and Teams restarted.
I should also add that I'm using Remote Desktop a lot, getting on my desktop machine via VPN from home and from conference rooms around my office. When I log into the conference room machines, they automatically launch Teams, so I have Teams running simultaneously on at least two machines at one time, one of which is displaying the other in Remote Desktop.
I'm hoping this last observation creates a possible repro case for Teams developers.