I've been running Sunshine on my Linux desktop for a while now and connecting to it with a SteamOS handheld and my laptop for mostly gaming for a while now. From what I can tell, the biggest difference with Sunshine and Moonshine when running on Linux is that Sunshine doesn't use a separate desktop instance per stream; by default, the streams will be mirrored to the clients, although there's a way to work around that somewhat by setting up a fake display output device with the boot parameters and a custom EDID with the specs you want (there's at least once repo where someone has a large set of them dumped from thousands of different monitor brands/models) and then setting up Sunshine to output when mirroring, which effectively means that only the remote client will actually have anything displayed.

It took a fair bit of iteration to get my setup to the point where it mostly works the way I like, but it's been pretty stable for months now. I game exclusively on my handheld streamed from my desktop, and on my local network the input lag is pretty consistently low enough that I don't notice any difference from when I had tried to play things locally on SteamOS, only I can easily max the graphics settings on most games I play (and on the rare ones that do struggle, there's often not a ton of downside to lowering the resolution a bit due to the handheld only being 1200p).