Whisk water, 1 teaspoon rice wine vinegar, 1 teaspoon soy sauce, cornstarch, sesame oil, and black pepper together in a bowl until marinade is smooth. Add chicken and marinate, about 15 minutes.

Stir chicken broth, 1 tablespoon soy sauce, oyster sauce, 1 teaspoon rice wine vinegar, and sugar together in a bowl until seasoning mixture is well combined.

Heat 3 tablespoons canola oil in a large skillet over medium heat; cook and stir noodles until golden brown and crisp, about 1 minute. Transfer noodles to a platter.

Pour the remaining 1 tablespoon into skillet with the oil; cook and stir chicken over high heat until no longer pink in the center, about 5 minutes. Add seasoning mixture, celery, carrot, bean sprouts, onion, and green onion; cook and stir until sauce thickens, about 30 seconds. Pour chicken mixture over noodles.