unable to connect the HP 1020 Laserjet printer with MacBook Air M2

Looks like this printer is not compatible with Macs.

HP – Software and Drivers for HP LaserJet 1020 Printer series

"Try manually selecting your Operating System. If your Operating System is not listed then HP may not provide driver support for your product with that Operating System"

The operating system menu only has selections for Windows and Linux.

HP Support – Printer Specifications for HP LaserJet 1020 Printer Series

No mention either of macOS support or of AirPrint support.

HP Support – HP LaserJet 1020 Printer series

Drilled down to the user guide, which says that the printer comes with software for Windows Vista, XP, 7, and Server 2003. Again, no mention either of Macs or of AirPrint.

About AirPrint - Apple Support

I see some printers whose names are variations of "HP Laser NS 1020", but no "HP LaserJet 1020".

HP 5.1.1 Printer Software Update - Apple Support

Earlier reports indicate that an HP LaserJet 1022 driver from this package can be used with an HP LaserJet 1020 printer as well, thus making the latter model compatible with Mac. However, it says Not compatible with macOS v12 and newer for the package in question. The problem seems to be that the installation is prevented with newer macOS versions, while the underlying driver as such appears to be OK. Various download modifications have been suggested for P1005, 1020, and other models (community search), but the success rate is somewhat unclear.

If a suitable HP driver for macOS 15 cannot be found, or if a modification is not possible, you may have to look for a workaround.

Linux drivers are available.

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 1020 act as if it were an AirPrint printer, in order to allow network printing from a modern Mac or an iPhone/iPad. Look upon this as an experiment.

Details about how to set up such a Raspberry Pi print server can be found in the posts by Techguyuk in Can’t print with iPadOS17 - Apple Community.

Tesserax reported about using a Raspberry Pi 3 Model B+ for an old HP LaserJet printer (in Can I connect my laser printer to my netw… - Apple Community).

What is happening? Have you tried to download the latest drivers to see if the issues persist ?