What is a driver and why does my computer not have one?

If the printer is Wifi and can talk (is talking) to the router, wifi for the computer should be unnecessary. The router will relay.

As I said, the steps are simple to establish if the printer is visible:
Login to router - did it assign an address to the printer?
Is the printer connected? Wired ok or joined to Wifi?
(More up-to-date printers will have a button/button sequence you can push to auto-join wifi, along with the button on the router.)
What is the resulting printer IP? Can you print a status page?
Open a DOS box on the computer. Can you ping the printer? This will prove the problem is not connectivity.

Can you then not discover the printer from the computer?
Or can you force the computer to add the printer based on IP address? (“Older device - add manually”)

When you say ‘wired’, what do you mean? Is the printer connected to the computer via a cable to the computer’s USB port?