I think Larian really failed making a Barbarian character with Karlach.
Truth. Growing up in the city rules out being a barbarian. Her character does need rage, but it would have been better if they made the beserker a subclass of fighter (and possibly barbarian too).
Some unique characteristics for barbarians that I can think of, that would make sense:
1. Support from their local god(s)/spirit(s)
2. Mastery of primitive weapons (bow, spear)
3. Intimidation bonus
4. Better at interpreting foreign languages (reading foreign scripts, eavesdropping on foreign agents)
5. Better at nature related things (plants, animals, weather)
6. Acrobatics bonus (climbed a lot of trees and jumped from rocks a lot in their youth)