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Definitely not 100% efficient, but it can still hit a much higher efficiency than without the heat recovery

100% efficient assuming a perfectly spherical combined cycle gas turbine with district heating circuit operating in a vacuum.

Let say all the loses provide heating for the power plant building itself. ;-)

The thing is that your home's heatpump has an efficiency of 300%-500%. So even if your power plant and power delivery only has say 50% gas-to-electricity-at-home, you are still looking at 150%-250% gas-to-heat-your-house efficiency.