Thank you all for your help.
It was the upgrade to the latest version of Big Sur (11.5) that messed things up.
Following your advice:
I reset the print systems.
I downloaded and installed HP Printer Drivers v5.1 for macOS
I tried to add the printer but it only found the "fax" version and it wouldn't print.
I went to HP and downloaded their HP Smart program. I followed their instructions to install the printer.
Again it only found the fax version and wouldn't print.
I reset the printer to factory settings.
Instead of using my regular wifi through the extender in my office I chose the wifi for the downstairs with a much weaker signal -- one bar instead of five.
Everything set up instantly with the one-bar distant wifi instead of the good wifi in the room with the actual printer.
It worked fine with the office wifi until the update to Big Sur 11.5.
Now it works fine with the downstairs distant wifi.
Technology is beguiling. But at least now it works.
Thanks again!