Note that the Model 3/Y can do 7kW on a single phase supply. This is what a typical home install wall connector will be with single phase.
Yep. The Tesla HPWC can do 32A single phase (7 kW) or 16A three phase (11 kW).
My HPWC is DIP-switched internally to 32A 3-phase (22 kW), but of course only delivers max 11kW to my car because the car is the limit. If it was connected to a car that could do 22 kW AC charging, I have no idea if the HPWC would actually deliver it, or whether the HPWC itself is also limited to 11 kW, in which case the DIP switch is a placebo.