Thanks for your prompt and thoughtful reply, Eric~F.
Well, it may be my fingers were not remembering the right strokes I used when it was working, though I had been succeeding accessing the switcher itself; so, yes, your instructions did get partial results initially: I saw that the app name was in the upper left of the Space I was in, but the switcher did not take me to the Space where my working document for the app was, so I still had to manually use control-arrow to get to that Space.
So...
I suspected it was not an app switcher problem but a Space management problem.
I checked my settings in Mission Control and the closest option I saw was "When switching to an application, switch to a Space with open windows for the application." I hadn't tried that since it didn't sound like what I wanted, and I don't know when that checkbox would have been unchecked since I don't consciously having de-selected it. Could it be the upgrade to Big Sur turned it off by default?
Thus your guidance didn't get me directly to the solution but forced me to rethink the problem and find the right checkbox.
Thus...you win!
Thanks so much, Eric~F. I am once again enjoying this what is to me delightful and critical tool for navigation and workflow.