Supercharger V2, of which there are thousands deployed and thousands more in construction (with a minimum of two chargers per site), are 145kW. Without any problem to the grid. Supercharger V3 is going to be over 350kW (exact power has not been announced yet). In order to move to the higher capacity, V3 chargers will have a battery buffer, and thus stress the grid less than V2. That is to say, they'll trickle charge from the grid (and their solar awnings, which Tesla is looking to make standard), then surge charge EVs.
Battery swap is a total non-starter for about fifty reasons that aren't worth reiterating yet again here. Every major corporate proponent has either given up on them or gone bankrupt. Including, by the way, Tesla, who was demonstrating their automated swapping system a couple years ago, but has since cancelled it. It's technologically possible, but grossly economically impractical (due to stockpiling requirements, made worse by the unavoidable necessity for widely varying battery profiles and performance characteristics, as well as the ever-changing technological baseline) and gets poor consumer acceptance in practice (as there's widespread opposition to giving up your good new battery pack for someone else's old degraded battery pack). There's also concerns about durability when you're replacing such a large structural element in the vehicle with HV connectors, although this issue comes in a distant third.