I am far from an expert, but I'm playing the demo on a Linux PC running Bazzite and it works well; if you aren't already, make sure you're running it using Proton. You can do that by going to the game in your library, open the settings for the game, go to the compatibility tab, and then check the box and make sure it's using proton.
A better option if that doesn't make sense or doesn't work would be to give it a bit of time for people to leave reviews on the website ProtonDB, and then check there; it's a dedicated site for helping people with Linux systems run games.
I hope something here helps!

i've had this issue with ttp2, try these launch options: VKD3D_FEATURE_LEVEL=12_1 VKD3D_SHADER_MODEL=6_6 %command%

Not working

Working