Heat pumps work fine on batteries. The better solution is extensive battery storage and (intermittent) grid power, under the circumstances.

They mention large hot water stores which are cheaper and simpler than batteries for storing heat, at least for now.

Exactly. Micro grids keep on functioning unless they are hit directly. Batteries can charge up when there's power from solar, the grid, rooftop wind, generators, EVs that can provide power back, and so on. There are many options here; batteries don't care where the power comes from. That kind of resilience is very hard to take out with drones once you have it. Centralized grids are much less resilient.

I expect Ukrainians don't actually need to be told this and are already getting creative with ensuring they have power. There's plenty of incentive there to make sure they are not overly dependent on centralized power and heating infrastructure. Of course it takes time to fix and upgrade all buildings; that's why the Russians can still have huge impact with their nightly strikes against civilian infrastructure.

I think Russia and Puting will get credited for inadvertently speeding up the energy transition across Europe by a few decades. Everybody is going cold turkey on Russian gas and the replacement isn't LNG. That's more of a stop gap solution until something more economical can be put in place. We're having pretty harsh winter here in Germany (and elsewhere in the EU). There's not a lot of talk about gas prices in the news so far. That's because we've had a few years to diversify our energy sources. LNG is now a big part of the mix, obviously. But the high price of that is also an incentive for people to consider alternatives like heat pumps.