Go back to basics so it’s actually usable in game without overloading the shader.
Make the cone into an alpha image.
Manipulate the alpha UV to enalrge/rotate/shrink the cone.
Base the fog out of the cone image by using it as the alpha of a lerp.
In your case (with the cone bring white) you’ll want to swap the lerp values around so that full fog is at 0 and no fog is at 1.
As far as rotating and managing the cone you have a billion options.
You need player location and player forward vector into the PP material, so probably use a MPC for it.
Making the cone via UV could also be performant if done correctly, but why waste effort when using an image is going to be faster and allow you to do any shape?