I would like to hook up with that question. As long as my knowledge goes, all video rendering is done via CPU, only the actual video output to a viewport and 3D scene rendering may be done by GPU. If there were a possibility to outsource the video rendering to the GPU, i would greatly appreciate to use it.
In the options, the only place were GPU/CPU usage may be configured is at "Edit/Preferences/System/Cycles Render Device".
My video card (GeForce RTX 2060) is able to on-the-fly render captured video on two channels (to twitch as well as youtube) alongside rendering a game, while the CPU is rendering the last edited video in the background. The GPU load by that twitch/youtube rendering is minimal (barely visible in the process explorer). Thus i would expect that the performance of video rendering, if blender could outsource it to the GPU, would be better by at least a factor of 10.
With the upgrade from Blender 2.9 to Blender 3.0, the video render performance per single video has been enhanced: It now uses all available CPU power. In Blender up to 2.9, only a part of around 1/3 of the available CPU power was used. Thus until today, i handled that by letting two to three videos render in the background simultaneously. But the render performance over all instances combined is still the same in Blender 3.0.