As no one on this forum seems to be "into" Apple, the following is a self-Q&A. A combination of my perseverance and willingness to try things out, and various suggestions over a four-day period from Matt at Universal Devices resolved the problem (for me). How you might ask? OK, with Big Sur you have to go to System Preferences | General | Prefer Tabs and set it to "in full screen" (not "always"; which is the default setting). After that, if everything else is working, you'll now see a normal UN/PW prompt screen. If you don't do this, you'll get a screen that seemingly only asks for your PW but your O/S is (nearly) fully occupied with the app and is non-responsive. So, the change in System Preferences (above) rectifies (and is needed) to move to Big Sur (and later).