So, if anyone cares, I've managed to run the game through Bottles on my SteamDeck
Use the Bottles Epic installer, enable the Bottles Runtime, Gamemode, Fsync and for the Runner choose caffe-7.10.1, dxvk-1.10.1 and vkd3d-proton-2.6. Then install the game through epic and run it there. After that you can just create a simple .sh script to add to Steam to be able to launch it there.
The only problem is that the text doesn't seem to scale down enough and so some of the UI overlaps. Wish there was an option for smaller displays.