The Le Potato AML-S905X-CC has h.264 and h.265 decoders up to 4k, emmc connector So you don’t have to run off an SD card. I’ve used it as a media player and its pretty damn solid. I can’t speak to streaming games because I don’t do that, so I don’t know if it’s a different format. It does not have a powerful processor, so if the stream is encoded differently I wouldn’t expect it to be very good.

Its pretty old, around rpi3 performance, but having the decoders in there make it better than the RPI 4 for playing those types of videos.

Raspi4?

$94 from PiAustralia, or $144 with a case, psu, cables, etc from RS. (both 4GB version, 2GB stock hasn’t been reliable since Covid)

Plays h.264/265 at 60fps fine, does 10bit too both via hardware accel, can play 1080p vp9 but it’s CPU decode only, can’t handle AV1.

2x minihdmi, USB-C for power (needs 5V 3A), 802.11ac and BT5, pcie ethernet.

Raspi5 is a lot more money and removed h264 hardware accel.

Anything listed on Jellyfin is usable.
Anything that can run an encode/decode with ffmpeg works with something like dispatcharr.

Regarding games: No idea. I think moonlight was/is a thing?

Is Open/CoreELEC OK?

Have a look at the DuneHD box. It’s an unlocked android box, CoreELEC support, kann play HDR and 3D content.

That is the cheapest solution I know.

Steam deck? Or an old laptop with bazzite?