Place noodles in a large bowl and cover with hot water. Set aside until noodles are softened, about 15 minutes. Drain and rinse thoroughly.

Heat oil in a wok over medium heat. Cook and stir onion and garlic until onion is translucent, about 5 minutes.

Combine rice wine vinegar, ketchup, fish sauce, chile sauce, peanut butter, soy sauce, lime juice, sugar, red pepper flakes, and cayenne pepper together in a bowl. Set aside.

Add shrimp to the wok. Cook and stir until pink, about 4 minutes. Add the ketchup mixture and stir. Move all ingredients to one side to clear a small space in the pan. Pour in eggs and cook without stirring until partially set, about 3 minutes.

Stir the drained noodles into the shrimp and egg mixture. Add 1/2 cup peanuts, 1/4 cup bean sprouts, and carrots. Cook and stir until noodles are heated through, about 2 minutes. Garnish with the remaining peanuts, bean sprouts, lime wedges, green onions, and cilantro.