"unable to communicate with the printer at this time" - Big Sur

I bought a new Macbook Air for my wife for Christmas, upgrading her old one which was running Sierra. The new machine is loaded with Big Sur and cannot communicate with either of our printers. (My own laptop, running Mojave, connects fine.) The Brother printer (MFC-J985DW) is listed by Apple as Airprint compatible. I reset the printer app on the new Macbook, removing all printers from the list, and then hit "add printer". Both printers (the Brother and the other HP printer) both showed up on the printer interface. (So the Wi-Fi network works.) I selected the Brother printer, and the "use" box came up with AirPrint. I hit "add" and a notice comes up: "An error occurred while trying to add the selected device. Unable to communicate with the printer at this time." The same thing happens with the HP printer. I tried connecting with the USB cable, but the Airprint option no longer shows up and it asks for a driver. (There is no Brother driver for Big Sur ... the company says to use AirPrint.) So I can't set it up using USB. What to do?