> with a electric heat pump you only need 1/6 J to get 1J of heat

The COP of a heat pump is not fixed at 6, it’s dependent on the delta T between the evaporator and condenser. As delta T grows, efficiency drops.

An air source heat pump will have a COP of 2 with a delta T of 70F/39C and a COP of ~4-5 with a 10F/5.5C delta T.

I’ve only ever seen a COP higher than 6 in a system that had a chilled water loop with chillers and cooling towers.