Wi-Fi doesn't work when ethernet connected

I understand Wi-Fi works, but only if you disconnect Ethernet. That shouldn't happen but you knew that already.

Try this: in Network Settings > W-Fi > Advanced... select all the networks that Mac has ever joined, including everything. You can "select all" if there are a great number of them. Click the [—] (minus) button to remove all of them. Confirm.

Then, join your wireless network(s) again. See if that fixes it.

Why do I have difficulty with Wi-Fi or Bluetooth devices when USB 3 devices are attached to my computer?

Some USB 3 devices can generate radio frequency interference that can cause Wi-Fi and Bluetooth devices operating in the 2.4GHz band to have issues communicating with your computer. Here are some tips to avoid this issue:

• If your USB device has a cable long enough that you can move the device, place it away from your Mac—and make sure not to place it behind your Mac, or near the hinge of its display. The antennas for Wi-Fi and Bluetooth are located there, and USB 3 devices placed there might interfere with your wireless connections.

• If you're using adapters or dongles on a Mac computer with Thunderbolt 3 (USB-C) ports, plug them into the front port on the left side of your Mac, or into the ports on the right side (if your computer has them). These ports are the farthest away from the antennas, making interference less likely.

• To avoid interference on the 2.4GHz band using Wi-Fi, try using the 5GHz band instead. You can change this on your wireless base station. Bluetooth always uses 2.4GHz, so this alternative isn't available for Bluetooth.

from:

About USB on Mac computers - Apple Support

Resolve Wi-Fi and Bluetooth issues caused by wireless interference

Resolve Wi-Fi and Bluetooth issues caused by wireless interference - Apple Support

all should work, regardless of which is at the Top of the list and providing your internet connection

...