More heat means more water saturation pressure, which means more moisture. It's just a natural phenomenon. If you stop your ghg factory for a bit you will see it stabilize at a new equilibrium.
makes sense, it just doesn't say that effect would be immediate since I am still at a point where the planet is below freezing everywhere, so I didn't expect that to start just yet
There is always some degree of sublimation / condensation, you are just getting a bit more sublimation with more heat. If you want to know more, the equation involved here is called the Penman's equation.