Does this information help focusing on the problematic component ?
Hardly a component, but maybe something.
Since it is restarting the fault is obviously not resetting its status, but consumed watts are very low.
If 0 watts is real there can't be any real higher leftover or memorized states.
Only thing that can have a sort of memory is a stand-by circuitry.
If power button is stuck and is constantly powering the thing there shouldn't be any stand-by possibilities.
For all normal situations power LED should also remain on.
Is there a setting how monitor behaves after power outage?
Setting that to stay off will reveal how power is actually going off internally.
If after that setting the monitor is still turning on the power is not really going off internally.
Power LED is many times connected to stand-by circuitry.
Measured wattage is also indicating that it's a stand-by circuitry that is acting up.
Is there any life in power LED when fault is on?