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I’ve started my C8, as well as my C7, several times w/the charger connected and have not experienced any issues. I leave the frunk opened slightly so as not to forget that the charger is connected and accidentally drive away.
Any number of people report having forgotten the charger was connected and trying to drive off. Though some report other damage, I don't recall anyone noting electrical damage to their car or charger.
I always disconnect first before even entering the car. I never start it with it plugged in. I have my charger strapped to a rack and I have nightmares where I forget and the whole rack comes crashing down.