Heat pumps work by using a high power pump to compress the working fluid from its gas state to liquid. This compression heats the gas to 30 C over ambient. That high temp is then cooled through coils to air temp (30C on a hot day). In the winter it runs in reverse. It takes expands gas which in the case of a heat pump fluid like R-410a boils at -48C, runs that -48C gas through the coils which picks up heat from the outside at -1C (48C hotter than the gas). It then compresses that fluid to 20C which is then released into the house. That's why heat pumps can freeze up in the winter. The cold cycle is so far below freezing that ice will form on the coils. So heat pumps switch to AC mode every now and then in the winter to warm up their coils to melt the ice off (while turning off the fan in the house). The need for a large temperature difference is why heat pumps don't work if it gets below -20C.

So a heat pump moves heat but requires a large temp difference which comes from the electric compressor. You also can't extract significant work from that heat difference once you factor the energy input of the compressor. Otherwise heat pumps would have a device to power part of itself from the heat that it is moving.