Not really, you mainly need it during the day for commercial demand. At the moment we're still in the phase of "negative demand" in almost all countries, where there's no question of storage and it just manifests as the ability to turn fossil power stations off. The UK has at the moment turned off most of its coal generation capacity for the summer.
What you'll notice is that Lignite (=Brown Coal)+Nuclear+Biomass+Water (i.e. the base generation) are sitting at the lowest point of consumption for the day.
Solar will only be able to increase (without storage) until there is no black coal used.
Correct, but Wind is already taking over large parts of the lignite part.
And the pumped water is storage for solar, btw.
For us as a society, it doesn’t matter if we end up with 100% solar, but only that we end up with 100% combined of Biomass, Pumped Hydro, Wind, Solar, Water.