So, you can probably rule out the motherboard. The PSU is still the number one suspect in my book. I'm assuming it's a new unit, right? It also should be able to handle the power draw from the RTX 4071ti.
One thing most people don't consider is the power and reset switch. If your computer just suddenly shuts down without even rebooting automatically, that rules out the reset switch. If the power switch somehow shorts for more than five seconds, it could signal the motherboard to shut the computer down. A sticky power switch could do that; you could rule this out by disconnecting the current power switch and substitute another power switch with a long wire that reaches outside the case (or leave the side panel off during this testing phase).
Another thing that bit me once is a shorting condition under the motherboard. I had one build where there was an extra standoff under the motherboard that I should have removed, but I forgot to. When I powered that system up, the standoff shorted to some traces and it created some sparks. That was a hard short. But you might have something in your case that's able to move around (maybe due to the fans moving air) and create a shorting condition. This is a long shot of course. You already pulled your motherboard and replaced it with another one, but your random shutdown problem is still there.
So, aside from hardware, can software shutdown a computer? Maybe if a setting in the BIOS for CPU or GPU over-temperature triggers, it might shut down the computer. There might be an app running in the background that tells the computer to shut down (we know that Windows will shut your computer down via software when you tell it to using the mouse).
Personally, I would try the power switch test first and then I would swap out the PSU if the computer still shuts off with the temporary power switch.
As Albert Einstein said, "I could have done so much more with a Big Al's Computer!".
