Connecting HP LaserJet P1008 printer to M4 Air

HP 5.1.1 Printer Software Update - Apple Support

Earlier, an HP LaserJet P1008 (1.6.1) driver was found in the old supported printer models information (that web page now only available via an Internet archive service). However, the package in question is Not compatible with macOS v12 and newer. The problem seems to be that the installation is prevented under newer macOS versions, while the underlying driver as such possibly is OK. Some package modifications have been suggested, but the success rate is unclear.

An HP LaserJet P1008 Linux driver is available elsewhere.

https://developers.hp.com/hp-linux-imaging-and-printing/supported_devices/index

If nothing else helps, you may want to investigate whether a small and relatively inexpensive Linux-based Raspberry Pi print server and CUPS could make a USB-connected HP LaserJet P1008 act as if it were an AirPrint printer, in order to allow network printing from a modern Mac or iPhone/iPad (an AirPrint printer can be used without additional drivers/software). Look upon this as an experiment.

More about how to set up a Raspberry Pi print server can be found in the posts by Techguyuk in Can’t print with iPadOS17 - Apple Community. Tesserax mentioned a Raspberry Pi 3 Model B+ in Can I connect my laser printer to my netw… - Apple Community.

It may very well have been working flawlessly for a decade on older versions of macOS where driver support existed, or on Windows where it remains supported. That does not mean that it will work on macOS Tahoe without drivers expressly compiled for this operating system and HP is not doing that.

AirPrint has a well-defined print server support section and may ignore a Raspberry Pi print server altogether. The P1008 laser is a device introduced in 2007 and should be considered for replacement with a modern AirPrint supported monochrome laser. Brother has some as low as $84 USD.