It does seem like a huge gap in the market somehow. There is just not one thing that supports both gaming and media well with modern features.
The oudated 2019 NVIDIA Shield TV Pro is still regarded as the best in class - despite not supporting many modern things like AV1, HDR10+, HDMI 2.1 or Dolby Vision.
I ended up using a Homatics Box R 4k Plus for everything video-related which _does_ support all of the above quite well, but it unfortunately has so many software issues which prevented me from using Steam Remote Play or Moonlight which is why I ended up settling on just using a docked Steam Deck for that use-case.
I switch between the two, which is pretty annoying!