> But electricity is under half (30%?40%?) and the rest of that energy isn't fossil-free.

The trick of course is that if you electrify heating and transportation they'll need much less energy. Your average car with an ICE has an efficiency of 20-40%, electric cars have 60-80%. Heating your house with gas has an efficiency of around 100%, heat pumps have 300%-500%.

In theory gas boilers for heating are above 90% efficient. Not 100% because to achieve 100% what you'd have to do is keep the exhaust gases (which are hot) inside, where the people are, and unfortunately the exhaust gases are poisonous so that's a terrible idea.

To hit 90% the boiler needs to be designed to condense water vapour out of the exhaust gases, this way we'll get back the energy needed to turn water into a vapour which is a large portion of the energy embodied by the exhaust gas. And to do that the vapour needs to pass a low temperature fluid, so we use the input fluid we were about to heat with the boiler anyway, we want this fluid to be cooler than about 55°C but that means if we're using the boiler to heat a home with radiators, rather than to make fresh hot water for cleaning etc. we need our return temperature from the radiators to be less than 55°C which means we need our flow temperature to be lower (than the typical 70-80°C programmed by builders, not lower than 55°©) or else the radiators can't possibly radiate enough heat to hit that number, which means we're actually doing much of the same heating efficiency work we'd have to do to use heat pumps anyway...

Not sure where you get your numbers but they are way off. Natural gas is 90% (nothing is 100%). Heat pumps are geothermal masquerading as electric. And the highest number I ever heard for a heat pump was 135% which was under nearly ideal circumstances. In Finland, heat pumps can't make nearly enough heat to handle a winter there so you need something else too or instead of.

Truth is that electricity is great for kinetic energy but terrible at making heat. Most forms of energy can be transformed into another form of energy at about 50%. Electricity is the weird one where its 90% to motion but only 10% to heat. So if you want heat, you want something that makes heat directly. That's why natural gas heating (for building and homes) is usually lower carbon any other method. When you try to switch to electric, it makes things worse because of these inefficiencies. And heat pumps are great when you are in the right environment for them (like say the UK down to say Spain or so). But in Finland, you are going to need more than just some pipes in the ground and a fan.