Hi,
Drivers from HP for the LaserJet 1020 printer appear to be available for Windows and Linux only.
You may possibly want to carry out a test using drivers for the HP LaserJet 1022 instead.
There is an HP 5.1.1 Printer Software Update from Apple. An HP LaserJet 1022 version 1.6.1 driver is listed in the referenced article Printer and scanner drivers for Mac - Apple Support. However, the System Requirements say Not compatible with macOS v12 and newer. If you try it anyway, it would be entirely experimental. It may not open/install/work with macOS 13 Ventura. So, do not expect too much from this.
You may have to reset the printing system between tests.
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)
As always, make sure that you have backup copies of all important files before testing anything. Software conflicts cannot be ruled out.