I assume everyone who happens upon this particular thread understands, this isn't a specific 1903 issue, but all Windows versions, nor is it only applicable to HP printers. Where I work, printing is like breathing air, it is the most important resource a computer can provide. I know, right.
My gut tells me that in the end we are going to have to get support from the printer manufacturers, that they will all most likely have to update their v4 driver code to accommodate the security vuln fixes Microsoft is pushing out to all versions of Windows right now.
you could try uninstalling and then re-installing the printer drivers (although that may not be fun for some people)
I actually had to do this with one of my HP printers connected thru a wireless/WiFi connection (it was the Hp envy photo 7858 printer) where I had to uninstall the drivers, reboot and re-install the drivers (and reconfigure the wireless connection on that HP printer itself thru the printer's control panel). now that "networked" HP printer works and I can print just about anything, even with the latest updates like KB4524147 for 1903/1909 and KB4524148 for v1809.
btw, my other HP printer (the hp envy 4500 series) is connected locally thru a usb cable and never had the print problems with the recent Windows updates.