big sur - printer compatiblility

The HP LaserJet Pro m402d is supported natively by Apple's AirPrint that is built into Big Sur. No need for any HP driver or software downloads.

Power on the printer and ensure that it is networked, either wired, or wirelessly. In System Preferences : Printers & Scanners panel, right-click on your printer's icon, and choose Reset printing system… . This will take you through the process of removing the printer, and re-adding it back with an AirPrint driver choice, rather than specific HP driver. Once the printer has been re-added, right-click on it again and choose Set default printer. Print something.

Try the HP print driver that Apple posted last Friday:  HP Printer Drivers v5.1 for macOS Dec 11, 2020