Try it.

On USB with the basic driver specifically, modern HP printers will let you use the device for exactly 10 print jobs before it locks all functionality and demands that the unit be connected to the network and an HP account registered.

Do not buy them. Find a brother instead.

Check your wireless config for anything that would block interclient communications. It’s common on wifi hardware to disallow wireless devices to talk to other devices on the lan. Different brands of kit call it different things. “Wifi isolation” is the most common.

Also, “you got a wireless access point”. What does that mean? Got it from where? Did you configure it yourself? Is it acting as a DHCP server? If yes, is it behind another DHCP server? Cause that’ll cause you issues like this as well.