I'm baffled here. Forget DS4Windows for a bit. Turn it off completely, and plug in your PS4 controller via USB. Do you get a "Wireless Controller" option to show up in the controllers list? It should show up, and should work, although it's Direct Input and not quite configured correctly.
From there, try starting the latest version of DS4Windows, while still connected via USB. Then you should have two more options show up in the game controllers list in LaunchBox.
Also make sure every other potential controller is disconnected when you run these tests, and reboot before trying them. That's a brute-force approach that should hopefully help.