Your GPU has a dedicated ASIC that can do the encoding simultaneously. On NVIDIA (not relevant in this case) that would be your NVENC encoder.

AMD and Intel have their own ASIC IP blocks that do encode/decode that's part of the GPU "SoC" but wouldn't consume GPU compute resources (eg CUs). That's how you see people already using GPU encode with obs (non-AV1 codecs) while gaming, and really that's how people like me using Sunshine/Parsec for the host PC for "remote" gaming (mostly for remoting into a Windows machine for the 1 game that cannot be run on Linux nor a VM due to anti-cheat). The only GPU resources you're using are PCIe bandwidth and perhaps some VRAM usage? But I wouldn't call it just dumping it from the CPU to the GPU, you have an ASIC that mitigates the brunt of the workload and AV1 with Sunshine has been amazing, can't imagine now using it for recording my gameplay vids will hopefully be better than H264 (due to lower bitrates and hence smaller file sizes).