Azure Stack HCI is based on Hyper-V. Basically they have the same virtualization technology.
Why vGPU can work on Azure Stack HCI but not Hyper-V? In theory, vGPU should work on both :(
This one should help: Partition and share GPUs with virtual machines on Hyper-V | Microsoft Learn
It is the decision of MSFT where they want to support GPU-P. Finally they will support it starting with Win2025 Server