homelab

That'll probably work. I used an old TP-Link 4 port WiFi router to do it. Flashed OpenWRT on it, set up the WiFi as client and bridged the ethernet ports off the WiFi. It's not fast, but works.

USB wifi from Aliexpress?

The cheapest solution, assuming you have a drill, a small jab saw, a measuring tape, an optional stud finder, and some sort of fishing line, is to run it in the wall. Then the only cost is the Ethernet cable, which is super cheap in bulk. You could do finished keystone jacks on both ends to make it look nice, but they aren't necessary.

Next to that the next cheapest is probably an old wifi router or AP to pipe the Ethernet from the poweredge into and then a wifi card in your computer.

Power line adapters are also an option.

I would run a cable

Do you have coaxial cable TV plugs in both rooms? Look into MoCa adapters that can get gigabit speeds. This could be a better option than power line adapters.