I’m not entirely certain what is working, and what is not, and which printing path is in use; vendor drivers, or AirPrint.
If the issue is limited to PDF files and other files print correctly, that’s usually a printer issue, or a vendor printer driver issue.
Confirm the printer firmware is current.
Reconfigure to print via AirPrint too, and not via vendor drivers.
Failing that, check with HP support for their suggestions.
if still not printing, I’d likely return the printer, and obtain a different model from a different printer vendor.
Whatever replacement printer might be selected, you will definitely want AirPrint support.