If that passes, it’s the power button (unlikely, it’s just a button) or the motherboard or some component. If the power button contacts are exposed, and assuming it’s a regular momentary contact switch, you should be able to bridge them to complete the power button circuit, eliminating the button itself.
It is a buttonless. So I plug in the cord, and the PSU will light up green for ~3 seconds and then turn off. It does not light up again. Does this mean it passed or failed the test?