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
Leaving a PC shut off like that to get it to come back on is either a heat issue or a PSU.
I have witnessed a Sapphire RX 6800 XT Nitro+ that would reliably crash the system the moment its junction temperature reached 110°C (not 109, not 111, always precisely 110).
This is a fairly high junction temp and sounds like a cooling issue. Try removing the side panel and see if the card stays cooler (want to see around 80C or so for junction, below 90C is okay. If the card is till getting to 100C plus on the junction contact manufacturer support as it sounds like the card is having a cooling issue.
The shutdown could still be from a PSU, as a CPU or GPU hits these higher heat numbers they can have increase power draw and it could be the PSU is not keeping up. However I would first look at that GPU temp.
