Do you have actual numbers for the COP factor for modern heating and cooling solutions? If its actually 5 (after accounting for transmission losses from power plant to building and other inefficiencies), then that means electric heat pump heating releases 3x less C02 than a in-building gas heater [1]. A solar panel solution will release like 4.5x (assuming 90% efficiency) less C02.

Finally, burning natural gas inputs additional heat energy into our atmosphere, with the gas-burner inputting 3x more heat into our atmosphere compared to the electric heat pump. A solar panel solution doesn't add more heat to the atmosphere. It takes energy that was going to get absorbed by the atmosphere anyway and concentrates it inside a building for localized heating. Except for the second hand effect of some of sunlight that would have reflected off from the roof back into space, now being dispersed as high entropy heat into the atmosphere.

Not to mention that if you use solar

[1] This is assuming that the power plant is a hybrid natural gas one (60% max efficiency) so 5*0.6 = 3. And the in-building natural gas heater is 100% efficient.