Hi,
It may be a good idea to reset the printing system. Does the operating system offer a suitable driver to use?
Reset the printing system on your Mac to solve a problem – Apple Support (UK)
Add a printer to your printer list so you can use it on Mac – Apple Support (UK)
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 supported AirPrint model listed in About AirPrint - Apple Support. However, the printer is in fact mentioned in an old (February 13, 2012) iOS: AirPrint 101 HT4356 article. It cannot be ruled out that the model in question was made for an older AirPrint version.
If nothing else helps, you could perhaps 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. Look for something like the HP LaserJet Professional P1100(w) version 6.9 driver in the Printer and scanner drivers for Mac - Apple Support article.
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).