Ventura conflicts with printers

It is HP's responsibility to provide updated drivers for new releases of macOS unless they have chosen to cease further driver development for a given printer. It is your responsibility to check with the HP printer website to ensure that they have provided drivers released explicitly for Ventura, and if not, do not perform the operating system upgrade — unless the printer is shown supported by Apple's AirPrint.

If the HP device is supported by AirPrint, and your printer is networked, either wired, or wireless, then you don't care about current HP drivers, but only with re-adding the printer and choosing AirPrint.

The HP OfficeJet Pro 9020 and 9020e are both supported by Apple's AirPrint. All you need to do is ensure a network connection, the device is powered, visit Ventura's Settings… Printers & Scanners panel, and under Printers, Click on the HP OfficeJet Pro 9020 entry, and on that subsequent panel that appears, click Remove Printer… and click Remove Printer again on the challenge dialog.

Back on the Printers & Scanners main panel, click the Add Printer, Scanner, or Fax… button. This opens a new panel and your HP OfficeJet Pro 9020 should be discovered on the network and appear. Click on the device name on this panel, and the Use: selector will activate with the printer description and you click the Add button to finish the setup. It now reappears on your main Printers & Scanners panel with a green active light and should be usable with Ventura at this point.

Same here. This just doesn't work.

I see the printer.

It seems to be connected via AirPrint but it dowsn't print.

I tried the above and when I go to add my HP 6960 all in one it doesn't appear as a printer to add. What else can I do?