Yes, because a heat pump is taking the heat from the outside environment and moving it into your house. You’re only paying the “transportation cost” and not the actual cost to generate heat. The heat was generated by the sun.

So the term efficiency with heat pumps typically refers to COP Coefficient of Performance. It a measure of how many watts of heat you are able to pump per given watt of electricity used. So 400% would be a COP of 4.0 which is definitely possible with air source heat pumps in milder weather and ground source heat pumps in pretty much any weather.

Yes, you might want to do some research on it.

The core idea is that you aren’t using 1 unit of electrical energy to create 1 new unit of heat energy. You are using 1 unit of electrical energy to capture several units of pre-existing heat energy from the environment and pump it indoors.

If I can spend 1 joule to transfer two joules of enthalpy from outside to inside, then that is 200% efficiency.

Burning 1 joule of gas would give you 1 joule of heat in a perfect world. That is what a non pump does.

More technically it would be a coefficient of performance of 4, which in some frames of reference is like 400% efficiency.

If you measure the efficiency of heat output relative to the electrical input power, then yes. The trick is that there's actually another input: latent heat in the environment. But given that this is abundant and freely available we don't usually bother to include that in our calculations.