I'm considering playing a Goliath barbarian, Path of the Beast. As I've played mostly arcanists since D&D 3.0, and when I DMed I trusted my players with their PC rules, I'm having a bit of a problem grasping purely melee interactions.
What I want to know is if, and how, these three features interact:
You count as one size larger when determining your carrying capacity and the weight you can push, drag, or lift.
Claws. Each of your hands transforms into a claw, which you can use as a weapon if it’s empty. It deals 1d6 slashing damage on a hit. Once on each of your turns when you attack with a claw using the Attack action, you can make one additional claw attack as part of the same action.
The Tavern Brawler feat (PHB, p. 170):
When you hit a creature with an unarmed strike or an improvised weapon on your turn, you can use a bonus action to attempt to grapple the target.
The rules on Moving a Grappled Creature state:
When you move, you can drag or carry the grappled creature with you, but your speed is halved, unless the creature is two or more sizes smaller than you.
So, could I attack a goblin or halfling with claws two times, after one of them (if successful) grapple a Small creature, and then drag it somewhere at full speed because I count as Large so goblins or halflings count as two sizes smaller?
If that matters, we play using standard array, and our expected levels of play are 5 to 10.