An electric heater uses 1000W of electricity to increase the energy in an air volume directly.
Heat pumps use 1000W of electricity to transfer energy from one area to another.
In the former case, the energy in the warmed air is entirely from the supply of electricity.
In the latter case, the energy in the warmed air comes from the intake air and the electricity is only used to move that energy around.
So absolutely a heat pump using 1000W of electricity can move 3000W of thermal energy from the hot side to the cold side.
This, by the way, is why you're absolutely right that efficiency is variable, as it depends on the energy gradient between intake and output.
An electric heater uses 1000W of electricity to increase the energy in an air volume directly.
Heat pumps use 1000W of electricity to transfer energy from one area to another.
In the former case, the energy in the warmed air is entirely from the supply of electricity.
In the latter case, the energy in the warmed air comes from the intake air and the electricity is only used to move that energy around.
So absolutely a heat pump using 1000W of electricity can move 3000W of thermal energy from the hot side to the cold side.
This, by the way, is why you're absolutely right that efficiency is variable, as it depends on the energy gradient between intake and output.