My computer shut down twice today while playing BG3. Exactly as OP said, I have to switch the PSU off and leave it for a few seconds and back on again to even get the power button to work again.
I've playing almost everyday since launch, and it has never happened until today. Maybe the most recent patch has something to do with that in my case as Erica pointed out.
Hardware:
Ryzen 5600x
RTX 3060Ti
600W PSU
