I'm not the biggest barbarian player, but I did build a couple barbarian characters in Pathfinder 2e (as far as flavor goes, the two classes are pretty much the same) that I really like and which went against the grain of all the barbarian stereotypes. The default assumption in Pathfinder is still the whole barbarian tribe idea, but for these two I went firmly against that. One I creates was a dragon instinct (subclasses are called instincts in PF2e) barbarian who came from a noble lineage of dragon-blooded sorcerers. Her draconic lineage ended up manifesting in physical might born from the rage and frustration she felt at a lifetime of being seen as lesser by her sorcerer family.
The other two were a spirit instinct barbarian, they basically manifest their rage through connection to the spirits of the dead in one way or another. The first was basically a dwarven crypt guard whose family had been charged for generations with guarding the crypts of their clan. As part of that they developed ways to open themselves up to their ancestral spirits to augment themselves in combat. He wasn't a barbarian in terms of culture, he was otherwise a very steady, typical dwarf in every other manner. The second was actually a knight in training who survived an attack of undead that killed the rest of his squad, leaving him haunted by their spirits, and his rage is essentially being possessed by them.
I use these two examples to demonstrate that the barbarian class does have more options open to it than it does at face value. To keep focused on 5e specifically, look at Critical role, their current campaign has a barbarian character that's basically a street tough with anger issues. I feel like as a class, the Barbarian is one that's most firmly tied to a very specific character concept, but it's possible to peel that concept away to first principles and try other things with it if you wanted to. However BG3 leans very heavily into the classic aesthetic and ideas behind the class, so that makes it harder to do in-game, even as they set things up such that your character breaks that mold by nature by coming from the city.