Germany currently generates 50TWh per year of solar
On average that's 136GWh per day, lets assume that was spread so that it's say 36GWh per day in winter and far more in summer.
It consumes 500TWh a year.
Lets assume consumption is 1,400GWh per day evenly across the year. Consumption is higher in the day, so even with shorter days in winter lets make that half during daylight and half at night, 700GWh each.
If Germany increased its solar to 50 times as much as it currently has to generate 1800GWh a day in winter, it would require 700GWh of storage and a total of 1400GWh during the day.
There are 48 million cars in Germany, lets assume that 65% of them are parked overnight and connected to the electric grid, making it 30 million cars. Make them all electric, with with about 30kWh of "flexible" capacity for draining overnight (50% capacity) and filling up in the day per car. That's about 1,000 GWh of storage available overnight, enough to provide for the entirety of German electric consumption overnight.
During the summer when solar capacity would be three times as much, that excess capacity could be used to generate green hydrogen through electrolosis, used to do things like aluminium production, could be exported to neighbouring countries.
Now sure switching cars to fully electric would increase total usage of energy, about 2,000 kWh per car per year, say 100 TWh a year extra, but then there's a lot of wind generation in Germany (>100TWh) now which would offset that.