Why do some people make one trait their entire personality?

It's a way for unimportant people to try to make themselves feel important and interesting.

Because that’s the only personality trait they have. It’s kinda sad

They are boring people who have no personality to speak of so they pick out one thing about themselves and build their entire identity around it.

They are pathetic and want to feel special.

Because social media turned their brains to mush and one trait is all they can develop and focus on.

because consumerism and false idols are what people like to attach themselves to when they do not have a spirit

It's not that crazy. People get consumed in their hobbies. If they don't do a lot of different things, they take that identity of "I do this".

This can also happen if they do many things, but they're either ashamed of the other things they do or put tons of extra importance on one thing in particular. Like, you have tons of hobbies, but you really love skating = "I'm a skater." You spend a lot of time woodworking, but you're infatuated with this blog you just started = "I'm a blogger."

Once that decision is made, it's actually kind of hard to break away from it. Depending on where it came from, it may require you to get interested in something else, or spend less time doing that thing. Think of it the same way as notoriety. If you got famous for doing something, how hard is it to become notable for doing anything else? DiCaprio will always be an actor, Hawk will always be a skateboarder, Bolt will always be a runner. It works pretty similarly in our own minds.

We just tend to fufu it if that identity is too basic (the most frequent point of contention since it doesn't involve actually doing anything; basically "I'm a human") or sounds lame ("I'm a social media influencer").

It's because they decided on an identity and after some time, chose that as an identity.