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.
It’s a mint problem. They still use really old packages and X11 for their display server.
If you tried again with a more modern OS and one specifically using Wayland, you may get better results.
Bazzite and CachyOS are built with gaming in mind.
Pikaos also great if you wanna stick with a Debian base but have up to date packages kernel and video drivers