Pokemon: An Unusual Traveler

Female protagonist, native to the world, no System. A slice-of-life Pokemon fanfic. No pairings, so ship whoever you like. The author's group battles are really bad, so I recommend skipping them.

Dongyun Zhao, who starts out with a brother who's a professor and sets off on a journey with the goal of becoming a powerful Trainer, thinks she's well on her way to achieving that dream.

But having to face a dark organization like Team Rocket right from the start is a bit too much!

Professor Oak: There are far too few diligent and capable juniors like Zhao.

Lance: I hope I get to work with her soon.

Ash: She's a powerful rival and a friend!