As much energy per time (say 24h), hence as much power. This is assuming the grid spreads the load geographically (not all the chargers at one place) and not everyone is rapid charging their car at the same time (impossible since there won't be enough rapid chargers).

"hence as much power" => "hence as much average power"

Under the assumptions, power equals average power (to a margin). It would be a huge mistake to try to build the grid to withstand the power of all existing electric devices at the same time, as the probability of such a situation is 0.