I've put a V860 III-S on my Sony camera, but when I try to use it in transmitter mode, I'm getting this weird icon on the LCD:
What does this mean?
It means you need to turn WL off on your camera to use the V860 III-S as an on-camera transmitter unit.
The WL setting is for Sony's own proprietary "smart" optical/radio system signalling. That's not Godox's system. Godox is basically hijacking the on-camera hotshoe communication and turning it into their own radio signalling.
It's counterintuitive, but with most 3rd-party radio flash gear, you have to turn off any wireless flash settings in the camera and have the transmitter on the hotshoe treated as if it were an on-camera speedlight.
The exception is if you shoot a Canon camera, since it's usually their proprietary wireless flash systems that's been reverse-engineered to create the 3rd party gear, and the 3rd-party gear can fake the communication the camera's expecting with its own-brand wireless flash gear.
IOW, on a non-Canon body, turn any wireless flash settings off. On a Canon body, you can use the in-body wireless flash settings.
See also: My Godox flash won't fire off-camera. What should I check?