The peak power draw will lie somewhere between your estimate (11.5kW/vehicle) and the typical estimate (920W), which would assume everyone charging at home. Clearly not everyone would charge at home (or with a 1kW charger), so the number is in between.

Both transmission and generation tend to cost mostly their peak usage. Generation is likely easier to upgrade, given a few years. I would imagine transmission is significantly more costly and complex, since the last mile network is enormous, but transmission likely has much more overhead (it has a soft instead of hard maximum as well due to simply increasing losses and increased thermal stress). I would say we probably are nearly prepared (with significant generation investments) if everyone charges at home at low power -- a 1-2 decade transition would go smoothly (my guess/estimate is 65% more average usage by that date). If most people opt for fast charging, the system will need significant overhaul (with widespread use of buffer batteries helping). It seems very wise for State incentives to increase capacity as soon as possible, to anticipate market demand -- the energy sector is likely slower than the automotive industry.