They're anti-nuclear and gambling that next winter is also mild. But the increase in electricity prices just increases inflation.
Battery storage is usually pumped hydro. If you have too much electricity (say due to strong wind at night when demand is low), you use it to pump water up a dam. When you need the electricity later, you open the dam and let the water fall on a turbine, and electricity is generated. Rinse and repeat.
RE: Here's the result of Germany shutting down it's nuclear power plants