The cable size doesn’t affect the breaker, if anything it’ll make it trip faster under fault conditions as you’ll be reducing your overall ZS value.
The CAT 5 is for the CT clamp meter which fits around the main incoming head meter tails, this allows the charger to see how much power the rest of your house is drawing, if it see’s that there could be an overload of the total supply it’ll drop the car charger down to a lower charge rate until the total house load drops.
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