Hi,
It may be a good idea to reset the printing system. Does the operating system offer a suitable driver to use?
Reset the Mac printing system to solve a problem - Apple Support
Add a printer on Mac - Apple Support
If not, you may want to try the Dec 11, 2020 HP Printer Drivers v5.1 for macOS (https://support.apple.com/kb/DL1888?viewlocale=en_US&locale=en_US) package from Apple. This download has been known to work with a number of models even under Big Sur. Look for something like the HP LaserJet Professional P1100(w) version 6.9 driver mentioned in the Printer and scanner drivers for Mac - Apple Support article.
Also, there is an HP Easy Admin tool for Mac that allows administrators to download drivers without a connected printer. If you need software from HP, and there is a problem with HP Easy Start or HP Smart, you may want to try this tool.
https://support.hp.com/us-en/document/c06164609
The HP LaserJet P1102w does not appear to be a model supporting the driverless AirPrint technology (About AirPrint - Apple Support).
If necessary, try a wireless connection instead of USB, or vice versa.
Before testing drivers, make sure that you have backup copies of all important files (documents, photos, et cetera).