What a charge point can do is signal to the car what the maximum AC current availability is, by varying the duty cycle of the Control Pilot signal. The charger(s) in the car then have to modulate the charge current drawn so that it is always within the maximum current that's been signalled. All charge current modulation is done by the charger(s) in the car, not the charge point.
Yes. I knew that.
The Tesla charger(s) seem to take several seconds to respond to a change in the maximum available current signal, so for days where excess solar generation fluctuates a bit, from passing clouds or variations in demand in the house, I found that the charger(s) weren't doing a great job of tracking.
...but I did not know this.
Thank you for the information.