W.r.t. heating did you also consider the effects of increasing local production as well as transferability and variability of load (e.g. requiring larger heat pumps and other "steuerbare Verbrauchseinrichtungen" to be "adjustable", which Germany does)

You don’t need to consider any of that, it’s simple arithmetic. Take the usable heat (volume of gas burned times efficiency of heater) generated by natural gas, convert to kWh (2.83 cubic feet is 29.3kW), and divide by 3 to approximate the heat pump size you’d need to replace the boiler or furnace.

Figure out how much natural gas was burned in a heating season. For every 2.83 cubic meters you need 10kWh of electricity to run a heat pump to move the same amount of heat as the natural gas was generating, assuming a COP of 3, given that 2.83 cubic meters of gas ~=29kWh

A 3 million BTU boiler will consume 85 cubic meters of gas in one hour running at max, or about 300kWh of electricity for the same amount of heat from a heat pump over one hour, assuming a COP of 3. It’s 360 amps of current at 480V three-phase (300kW/480/1.732 = 360.8A), or ~400 horsepower.

Where I live, 85 cubic meters of gas costs about $9 and 300kWh of electricity costs about $45. Natural gas still wins in cost even if your NG heater is only 25% efficient. Even though the heat pump is 3 times more efficient, it costs 5x as much to run (at maximum, variable speed compressors will make the COP of the heat pump in practice better than 3 but it will still cost more to operate.)

It’s a straightforward thermodynamic equation - x fuel burnt (and useful heat from that) vs maximum theoretical efficiency for heat pumps for equivalent heat.

The reality is likely worse for a number of reasons, but even if way better it doesn’t get around that you’d need many multiples of the entire electrical grids peak capacity to come close. And that is assuming there is zero other load on the grid, which isn’t going to happen.

If everyone completely redid all their structures and all their use of heating, and installed all the best heat pumps, AND doubled grid capacity, maaaaybe. But we’re talking massive amounts of Capital. Capital that used to be cheap, but isn’t anymore.

Far more Capital than likely has been spent so far on renewables too, but it’s hard to calculate it because of the sheer distortion that it would cause trying to do something of this scale.

It might be legitimately cheaper to buy Northern Africa and move all Germans there instead (in new construction). That seems pretty unlikely for sócio-political reasons though.