Turns out it is not the PSU, it's the motherboard 😢
Although this has actually been a rather satisfying mystery to solve. I wound up doing the "paper clip test" on the PSU to confirm that it works, and then used a multimeter to do a connectivity check to confirm that the power and reset switches are working, then I shorted the power switch pins on the motherboard to simulate pushing the power button and poof, nothing happens.