The effects of electric battry density is cumulative. A lot of the requirements come from hauling the battery. If the battery gets smaller, you also need a lot less energy
Yes that too, lower battery weight means the rest of the aircraft can be made lighter. It's been a long time since I've seen numbers but the effect is more significant than people would naively assume. As you increase the weight of component you need to also increase the wing area and the required power. Which itself adds weight.