I think that maybe this could actually work, almost.
Feel free to ask questions about this here, but for expediency, an explanation of the theoretical operation of this Maxwell's Demon can be found here:
https://stirlingengineforum.com/viewtopic.php?f=1&t=5338&p=18503#p18503
IMO, and I've studied both heat pumps and heat engines for a very long time, your comment only demonstrates a lack of understanding regarding the details of how either machine or appliance actually operates.
These "Ideal" scenarios of a heat pump actually being a heat engine running backwards are about as silly as saying: if you turn the crankshaft on your lawnmower backwards it will produce gasoline.
A heat pump running backwards is an air conditioner. All either one does is move heat