The problem is that the printer driver is not signed. I can’t install it, unless I go into Terminal and use
sudo spctl --global-disable. After installing it this way, the printer driver still does not appear in the Bonjour Printers & Scanners settings.
The download from HP also contains PPD files, which as a workaround I updated
/Library/Printers/PPDs/Contents/Resources/, but when macOS wants to complete the installation, I get an error alert saying “The printer software was not installed correctly. Please reinstall the manufacturer’s software.
Is there a way to process the PPD file to make it work? Or does that mean I won’t be able to run that old printer in Ventura? It’s a nice printer.