The article doesn’t go into it, but a key advantage they have is that heat pumps move heat, rather then trying to generate it. So they can move a lot more heat into your house than would be generated by running the electricity they use through a resistor. This makes them effectively more than 100% efficient (the exact amount depends on temperature) as compared with burning a fuel or resistive heat.
It is really not hard. Heat pump coefficients of efficiency floor at 1, but typically range between ~2.5 and 7. That is, for every joule of energy they consume, they pump 2.5 to 7 joules of heat into the conditioned space.
So you have to just look at efficiencies involved.
Still, we’re just summing stuff. And while I won’t pretend any napkin math here is the same as a formal research project, we can plainly see that the HUGE energy efficiency of heat pumps can easily eclipse the inefficiency of fossil electrical production, all else being equal. Of course, whether it actually WILL be better than a fossil furnace will depend on local factors, but these places are increasingly becoming edge cases. And then, on top of that, you unlock future potential to seamlessly switch fuel sources from fossils to renewables, which becomes very important in lifecycle cost analysis.
This is the same reason electric cars beats ICE (gas driven) cars even when charged on coal power. Big coal plants and the distribution grid are more efficient than small scale car engines.
You need combustion engines to be BIG to get past 30-40% efficiency ranges, but the really big power plants can just perform efficient burns and heat water to drive efficient turbines, which is impossible in cars. And the rest of losses in electric cars are either minimal or equivalent, so you get a big net benefit.
Even better than that is an electric bus and other public transit!
Even better when your busses/transit are powered by a pantograph.