As for control, there are proprietary and OSS solutions (shout out to https://evcc.io/en/) that allow you to control the charging process based on price, grid load, local PV generation, etc.
That's alarming. There's no way the car can know that there's another appliance on the same breaker. The only way it can know it should decrease its power draw, is by detecting that the voltage decreased on the circuit, but that voltage decrease will only be noticeable if the wiring is undersized for the load (in fact, that feature is probably designed to protect against overheating undersized wiring on the circuit feeding the car). That circuit is probably severely overloaded, which can be a fire risk.
They might be using one of these: https://www.chargedfuture.com/240v-outlet-smart-splitter/
There’s also smart breaker boxes that again have nothing to do with Tesla specifically. The breaker box will preferentially shed EV charging first when someone would otherwise trip their whole homes’s connection to the grid. It’s not a perfect solution, but sometimes your local utility doesn’t want to upgrade your connection to the grid because their substation is fully provisioned or whatnot.