Heat pumps are pretty great, but as of today, they are by no means necessarily more efficient than burning gas directly for heat, at least when it comes to GHG emissions. In fact, in very cold climates where air temperature is below freezing most of the time, air-source heat pumps are highly unlikely to be more efficient than just burning gas, unless we move wholesale to nuclear for electricity (solar won’t help you during winter, and wind is too fickle to solely depend on).

Also, gas furnaces get those 99+% efficiencies only at input=output (ie no heating) temperature. Most radiators require a water temperature well north of 50C to emit the power required, and for decades gas furnaces were thus set to default output temperatures of 70-80C. At that point, the maximum thermodynamic efficiency (which is a curve as function of temperature differential, with the optimum at Tdiff=0, ie no technical improvements are going to improve this) is more like 70-80%. Actually, a cheap way to get a ~10% gas bill reduction is to change the output temp to 50C (if yours runs at 70+) and see if your radiators still can emit enough heat to reach your desired room temperature.

Long term, heat pumps are the only sane choice. Burning gas in a plant and running a heat pump off its electricity is more efficient that burning it yourself. In fact, as of next year (or was is 2024?) any gas furnace must be replace with at minimum a hybrid heat pump here in the Netherlands.