I found that llms can be useful in troubleshooting.
Maybe start with comparing hardware sensor stats GPU/CPU temp/frequency/fan etc.
I think is useful to use a bleeding edge OS since what you are talking about, is a combination of kernel/drivers, user space tools and software.
Start with something low level maybe clpeak or as part of Phoronix Test Suite. A game is a complex software that touches many parts of a system, especially for laptops where some resources are shared.