Heat vegetable oil in a large saucepan over medium-high heat; saute onion, mushrooms, and garlic until tender, 5 to 10 minutes. Add water, rice noodles, and chicken bouillon to onion mixture; bring to a boil. Reduce heat to low.
Mix shredded chicken, green onions, and cilantro into soup; simmer for 5 minutes more. Transfer soup to serving bowls and top with bean sprouts, a squeeze of lime juice, and Sriracha hot sauce.
