honestly, “efficient” can imply several things, and they don’t seem to clarify what (at least from my first pass of this doc).

How would you like to define it?

How about this for an analogy - which of these two is more efficient:

1. Plant some wheat in your back yard, buy fertilised eggs to hatch into chickens, plant tomatoes and basil, plant an olive to grow a tree, and eventually, years down the track, you can make yourself a bowl of pasta.

2. Notice your next door neighbour already cooked some pasta and made more than they can eat. Ask politely and they'll just give you a serving.

Obviously - the second option is more efficient, and that's effectively what a heat pump does. They don't heat up your home, they just take a bit of heat from the air outside and move (pump) it into your home. It's far far more efficient than creating new heat from scratch with a gas system.

Exactly how much more efficient will depend on the outdoor and indoor air temperature, and on the brand/model of heat pump you buy, and other factors (such as the length of the pipe between the outdoor unit and the indoor unit). You really should ask for specific advice on your home - but in general, a heat pump is extremely efficient.

Where I am, electricity is pretty cheap, but natural gas is tremendously cheaper per jule… so we can actually pay less by using the “inefficient” fuel for our home.

Have you actually looked into it, or are you just making assumptions?

I can tell you that my heat pump, in my house (yours will be different), in my climate, adds about $5 per week to my electricity bill. Is your gas bill less than $5 per week?

Or at least - that's how much it cost before I had solar panels. Now that I have solar... it uses about 20% of the power typically produced by the solar panels on my roof leaving plenty of excess power that we sell to the grid for about the same amount of money as what we spend buying power overnight. Since we installed solar our entire electricity bill is about $0 (and we use power for a bunch of other stuff, including to cook breakfast and dinner when the sun typically isn't shining*). We don't have a large solar system either - in fact, installing solar cost less than installing heat pumps.

(* our solar system comes with instruments and software to measure our consumption - and I can tell you that heating up a family meal with an electric cooktop uses more electricity than heating an entire house with heat pump... because the cooktop is creating heat, and the heat pump is simply moving heat)