No Need to Panic
Are you assuming everyone would need a complete fill up every day at 350GW chargers.
Average mileage per car per year is about 7500miles or 12000km. this is only 32Km/day. The car mentioned can do this in approx 100/700*32 or 4.5KWh a more realistic gold id.3 will do this in 8KWh. 23million registered cars = 184GWh per day, a lot of these will be overnight so assuming it averages at a 8 hour charge this will mean a maximum of 23GW/hr is required, this is quite easily achieved on the grid at the moment, and considering they will have 10-20 years before this capacity is fully reached and during that time the BMW type of efficiency may be achieved along with reductions in other energy usage, this should be easy. Of course there will be HGVs as well being replaced needing a bit more but my guess would be a lot of people would start installing solar PV with local battery storage which would reduce the load required on the grid.