It seems it supports DP 1.4 as well, so perhaps you could get an adapter if your display only supports HDMI 2.1
There are two kinds of DP to HDMI adapters. The passive ones are like you said, they need special support on the GPU (these ports are usually labelled as DP++), IIRC they only do some voltage level shifting. The active ones work on any DP port (they don't need AFAIK any special support on the GPU), and they do the full protocol conversion.
Club 3D active adapter: https://www.amazon.com/Club-3D-DisplayPort1-4-Adapter-CAC-10...
I’m using the Club3D active adapter, which is the only one I found in reviews to reliably work. And it does, 0 problems whatsoever.