Whether or not it's inside the GPU die would depend on if the display controller is part of the GPU die or not. On a mobile SoC everything tends to be on the on

Whether or not it's inside the GPU die would depend on if the display controller is part of the GPU die or not. On a mobile SoC everything tends to be on the one die anyway so... sure. On a discreet desktop GPU I have absolutely no idea. They might not even bother having one at all? The mobile ones though are pretty good, though. They can do like ~6 composition layers with alpha blending, cropping, rotation, and apply a color matrix for display calibration. All in the dedicated HWC silicon, GPU can be powered off (or doing something else like rendering a game)