Combine water, brown sugar, vinegar, soy sauce, sesame oil, garlic paste, fish sauce, and oyster sauce in a bowl. Dissolve tapioca flour in soy sauce mixture to make the sauce. Set aside.

Heat sesame oil in a large wok. Add bell pepper, mushrooms, and onion. Cook, stirring occasionally, until vegetables have softened, about 5 minutes. Add chicken and cook until chicken is no longer pink inside and juices run clear, about 5 minutes. Add sliced garlic; cook and stir until garlic is fragrant, about 1 minute. Pour in sauce. Cook and stir until sauce thickens slightly, about 5 minutes.