But I'd venture to say the statement "most electric heaters are heatpumps" is in fact false. There are a lot of heat pumps in the world, but there are also a lot of pure resistive electric heaters. I suspect that most things people call electric heaters are resistive electric heaters.
If a Stirling engine can be operate at 50% efficiency and a heap pump can operate at 400% efficiency, could we take a source of heat (e.g. heat side product of computation instead of burning fuel) use it to power the Stirling engine and use the movement of the Stirling engine to power a heat pump and thus turn computation into house heating at effective 200% efficiency? (under whatever assumptions were made in the claim of 400% efficient heat pump; I assume the temperature differential is key; I also assume that the optimal cold side for the stiling engine and for the heat pump is quite different, but you can tap one in cold air and the other in deep ground)
A heat pumpt doesn't generate heat, it /pumps/ it from one location to another. It can only achieve above-100% efficiency if you don't include the source of the heat in your calculation.
For a more practical example, consider a (simplified) geothermal heating system. It consists of a probe that's drilled some 10-15m into the earth, a radiator in your living space as well as a pump and piping connecting the two. The earth's temperature surrounding the probe is relatively constant at 10-15 degrees C.
In winter, when the outside temperature falls below those 10-15 C, you pump warm water from the probe into the radiator. Using the example numbers, 100W of electrical energy might provide you with 400W of heating output. The 100W has no part in generating the heat though, it only moves it from the warmer probe to the cooler radiator. The reverse applies in Summer, when the surface temperature is higher than 10-15 C.
What you're describing exists in the form of district heating. Heat is generated in a central location (e.g. as a side product from garbage incinerators), and a heat pump is used to transfer the thermal energy from that location into a bunch of surrounding houses. But, in any case: the whole process only makes sense as a way to capture excess energy from the heat-generating process; and you are always limited to (at the theoretical maximum) capture all of the excess energy output, but not one Joule more.