Starting is really not a very tough action for loads. As others have said, either actuating the starter turns off the lighter socket or you get get the cold cranking droop which can go pretty low on a very cold morning- 6V isn't unusual.
The tougher actions are what are called "load dumps" where a large load is turned off and the alternator is cranking out a bunch of current, this is where you can the big spikes. The bad loads are the AC compressor magnetic clutch, power windows and seats or a loose connection to something like headlights or a loose connection in the charging system. Each connect and disconnect causes a good spike with a lot of energy. Since about 2015, a lot of the better cars have a central suppression system, a monster tranzorb like device that is up stream of everything usually in the charging system or before the main fuse block.
My best advice is to use good quality accessory adapters. Don't use the ones from the dollar store or a gas station. The good one's have some decent surge protection. Don't ruin your $1000 phone trying to save $20 on an adapter.
If you're curious, there is an ISO spec numbered ISO7637 that lays out all the horrors of vehicle power distribution. The real spec costs money but there is a pretty good wiki and some other resources on line. ISO 7637 is the parent spec of some other specs that it references for charging system and trucks. Trucks are really bad.