I looked at the support page to which Rudegar linked, and there are no macOS drivers there. Only Windows ones.
While Monterey is "out of date" (no longer one of the most recent three), I don't think that's the reason that there is no driver for your printer. In my experience, printer manufacturers do not remove old drivers from their support sites just because new operating systems come along.
The good news is that the printer's Technical Specifications page says this (emphasis mine):
HP Support – HP OfficeJet Pro 8135e All-in-One Printer
"Mobile printing capability
Chrome OS; HP app; Apple AirPrint™; Wi-Fi® Direct Printing; Mopria™ certified [4]"
If a printer supports AirPrint, you do not need separate drivers. Any recent version of macOS (including Monterey) should be able to print to it, using the support built into macOS.
About AirPrint - Apple Support
Connect an AirPrint printer to a Wi-Fi network - Apple Support
Add a printer to your printer list so you can use it on Mac - Apple Support
HP printer setup (Mac built-in driver) – HP Support