I've had the same problem when trying to print out a report tonight. Also, I uninstalled then reinstalled my HP Officejet Pro 8210 printer multiple times. One is able to print the test pages, but when it comes an email or another kind of file (PDF for example), you receive the error code 0x800706ba or 0x80070709. Looking at the printer under devices and printers, what is missing is the driver. It affects if you use the 8210 as a network printer, ethernet or wireless. It works well for me as a USB printer. The whole idea of a network printer is that you can print from another room, or print from your tablet or laptop without having to run to your printer and connect via USB cable.
While it seems the problem dates back to KB4522016, I suspect it may go back to the September Patch Tuesday or earlier if reports of those not installing 4522016 are experiencing print issues.
Hopefully a real fix can be found.