This is making me wonder if there is a product that just... streams things well for you. I hate my Chromecasts, but it's the best solution I've found for what I want.
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!