In windows you’re not sending the signal directly through another port. You’re sending the dGPU’s signal through the iGPU to get to the port.
On a laptop with nvidia optimus or AMD’s equivalent you can see the increased iGPU usage even though the dGPU is doing the heavy lifting. it’s about 30% usage on my 11th gen i9’s iGPU routing the 3080s video out to my 4k display.