Hi,
Thank you for the information.
Yes, the latest software from HP for the HP LaserJet P2055dn Printer is for macOS 10.12 Sierra. I assume that the HP 5.1.1 Printer Software Update package from Apple was the one that you tested. It is true that the system requirements for this download indicate that macOS 12 is not compatible, but according to some reports, at least a few other HP printers seem to have worked with this package (with earlier Monterey versions) anyway. What I had in mind was to test something like the HP LaserJet P2055 with Duplexer 19.13 driver mentioned in the Printer and scanner drivers for Mac - Apple Support article as an experiment only (software conflicts cannot be ruled out, so it is important to have backup copies of all important files before testing anything). However, if this is what you have tried, please disregard what I just wrote.
Have you also checked whether generic PCL printer software appears under Use: ? Alternatively, could drivers for another (similar) HP laser printer model be found/tested?