Last time I tried to play Stray on Linux Mint on my laptop while connected to 4k TV, I ran into severe degradation unrelated to thermal throttling. I had to tweak the resolution down a lot and even the graphics. I recently went back to using Windows on the laptop because of an unrelated network speed unreliability problem on Mint, and when I tried Stray, there were no issues. Before this, I had even installed Stray on my gaming PC to stream from the laptop because of how laggy the performance was.
Specs
RTX 3080-Ti Laptop AMD Ryzen 9 6900 HX Linux Mint latest 16GB RAM
EDIT:
Okay so I suspected it was thermal throttling, even though I have a cooling fan. Turns out not using a cooling fan is better than using a cooling fan at the lowest setting. At the highest setting, the cooling fan is too loud but the game performs still slightly worse than on Windows.
Personally I think it’s either not the right drivers or the software that controls the fans is working against you. My advice is to tweak the fan curves in BIOS since it probably uses that. Also check wiki and forums on how to tweak fans, either manually or with a tool.