This answer is incorrect, but I'm not deleting it because the historical context may be interesting. For a Windows solution see @Silbee's answer. Non-pro edition of Windows probably supports this too, but you need to know the registry key corresponding to the gpedit setting.
In the Windows 95 era computers didn't turn off after OS shutdown because it wasn't physically possible: the power button wasn't a momentary switch, ie. it connected its two terminals in one position and disconnected them in the other position. You had to manually press the button again to physically cut power.
With the advent of ATX and ACPI standards things changed a bit and the power button is momentary now: when it's pressed, terminals are connected, but as soon as you release it, they are disconnected. The motherboard is responsible for sending the "power on" signal to PSU and maintaining it. The protocol got slightly more complicated, but it's more flexible and safer now. For example the PSU can safely turn off the power when it's overloaded.
Long story short, hardware has been completely incompatible with what you're trying to achieve for the last 20 years.
Maybe your BIOS has hidden advanced menu or can be modified to expose the option you need. It would void the warranty though.