
Native
It just works.

Major slowdowns on Native, Proton works great.
The native version didn't seem to use my GPU much which caused major slowdowns, especially when zooming in. The Proton version ran fine and used my GPU correctly.

On higher populations (over 10,000), I experience 20 ish FPS.
I recommend a 6 core CPU for this game, even on the lowest settings I had issues running larger worlds, all while my GPU floated in the 20-30% range. I also recommend more than 16GB RAM.

Works great
When i get an achievement it would sometimes show me a stretched and enlarged partial terminal window. I just press escape and it closes and continues without a problem.

gamescope -f -w 1920 -h 1080 %command%
There was very bad latency without gamescope
The game usually crashed when i tried to move around the camera without gamescope
I don't know what causes the instability, could be Sway or Wayland, but the native build was instable for me when not run in gamescope.
Works as if it's on native.

Some UI elements flicker sometimes
The UI elements on the far right of the screen are not interactable

the game wouldnt launch for me on linux without using proton, but when i did many ui elemants were missing.
some backrounds for ui ellemants and the tab sellection buttons are gone

NOTE: You no longer need NCMS. It's no longer maintained. You should use the alternative to NCMS called NeoModLoader as it natively supports Linux and all the mods that NCMS supported but you do need to compile it manually as I couldn't get the prebuilt binaries to work.
To Compile and Use NeoModLoader:
Install dotnet-sdk
Clone NeoModLoader's repository
Run dotnet build ./NeoModLoader.csproj
(You may need to modify prepare_debug.sh for a successful compilation)
Installing mods is way more complicated to do as you get all sorts of path resolution issues, especially with CollectionMod. But it does work.
In-game windows have weird click bounds. Not sure if this is a KDE Plasma issue.
The Linux build of this game may require some extra work.

Native
It works perfectly out of the box

For NCMS to work, I had to force the use of proton experimental

the official and unofficials layouts were way too difficult to use, i don't even know how people can play this game without keyboard/mouse
definitly not recommanded to play on steam deck without a mouse and a keyboard
Proton adds compatibility for community made mods. Native has not much mod support but is just as stable as Proton. This was on experimental, but they should work on the stable releases.
The native linux version is flawless but in order to get mods you need to use proton (which is also flawless)

Very stable and its native to Linux!
Would recommend
Works out of the box
Works smoothly no problem, no configurations just download and play!
Touchpad didn't work. Using an external mouse did work though