Some chargers communicate directly with the energy supplier and charge at the cheaper rates.

You can do this yourself as well with home assistant (if your charger supports it) and some API calls. It's just a matter of telling the charger when to start and stop the charge. The rest of the communication between the charger and the car is some protocol I can't remember the name of.

Could be wrong but I guess it more likely communicates with the charger. The car will always try to draw if it's plugged in, but most chargers can be switched on ("charge") and off ("don't charge") remotely. It's probably quite trivial to have something watch the price of power and on/off as appropriate

Energy providers use whatever internet API there is for either chargers or cars.

Octopus UK has a list of charger models and car brands they support for their special tariff for cheap off-peak EV charging.

The charging cable has a protocol for negotiating power, so either side can pause and restart charging.

My car hits the api for my power company and knows how much charge it needs and plans out its charging schedule, always avoids peak.

No the smart meter communicate with the charger.