I’m not a wrestler or a wrestling fan, so no clue for most of them. Bars and holds… well, I think the automatic damage to the grappled creature that is dealt with the unarmed fighting style is meant to symbolize damage dealt by various holds and bars, so that would apply here.
Airway chokes are extremely impractical in D&D; every creature can hold their breath for a number of minutes equal to their CON modifier with a minimum of 1, and that means 10 rounds. I wouldn’t bother trying to simulate that, just deal the 1d4 damage and move on.
Blood choke… well, that’s a different matter entirely. I would most definitely require the grappler feat and the unarmed fighting style for this. Say, you forgo the automatic damage to the grappled target and instead force the target to make a CON save, DC = 8 + your PB + your STR mod. If the target fails, it gains a level of temporary exhaustion (that lasts while you’re choking it), if it fails by more than 5 then it gains 2 levels, and if it hits 6 levels it falls unconscious.