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.
I found the switch quite easy from Windows to Mint. Think the reason it is recommended so much, as it makes the first step into Linux easier. But as you said it has it limitations in gaming.
I ended up with two distros, Bazzite for gaming and still using Mint for office staff.
As I have to say the performance and speed of Mint distro is much better, for just doing my day to day things.