Heat pumps have a COP value of around 4 to 5 (10 to 15C outdoor) and 3 (0C outdoor). The seasonal COP (or SCOP) measures the efficiency over a whole season, and that typically sits around 3 to 4. That means that for 1kWh of electricity a heat pump delivers 3 to 4kWh of heat to the house.

Burning gas to heat a home means "1kWh" of gas, delivers ~1kWh of heat.

Modern gas power plants are about 55 to 60% efficient, so "1kWh" of gas becomes ~0.57kWh of electricity, which after transport losses (-6%) arrives at the home as 0.52kWh, which gets turned into 1.5 to 2.0kWh of heat.

=> It's almost two times as efficient to turn gas into electricity and use heat pumps in the home

But a gas burning furnace can have 100% efficiency, that is trash compared to what I get from a heat pump considering a gas power-plant (60%) * national grid efficiency (90%) * heat-pump 500% efficiency where I am (combined efficiency around 270%, or 2.7 times the gas furnace).

The only gas-based solution to get close would be using a gas generator at home (30%) to power the 500% heat-pump, and routing the 70% of waste heat inside (to get a combined 220% efficiency).

But that heavily depends on the heat-pump efficiency, which will depend on your ambient heat and instalation.

The ceiling is not 100% efficient, when you have a heat pump.

Also, the US residential gas infrastructure leaks ~1% of the gas it moves. That sounds like nothing, until you account for how unburnt ch4 is ~80 times worse than co2 on a timescale of 20 years.