Combine vinegar and serrano in bowl. Let sit at room temperature for at least 15 minutes. (Chile vinegar can be refrigerated for up to 3 days.)
Using highest sauté function, cook 3 teaspoons oil and garlic in Instant Pot until fragrant, about 3 minutes. Stir in 2 cups water, oyster sauce, sugar, and fish sauce, scraping up any browned bits, then stir in chicken.
Lock lid into place and close pressure-release valve. Select high pressure-cook function and cook for 9 minutes. Turn off Instant Pot and quick-release pressure. Carefully remove lid, allowing steam to escape away from you.
Meanwhile, place noodles in large bowl, cover with boiling water, and let soak until almost tender, about 8 minutes, stirring occasionally. Drain noodles and rinse under cold running water until chilled. Drain noodles well again and toss with remaining 2 teaspoons oil; set aside.
Using slotted spoon, transfer chicken to cutting board. Let chicken cool slightly, then shred into bite-size pieces using 2 forks. Add green beans to broth remaining in pot. Partially cover and cook, using lowest sauté function, until green beans are crisp-tender, 3 to 5 minutes.
Turn off Instant Pot. Stir in noodles and chicken and any accumulated juices and cook, using residual heat, until noodles are tender and chicken is warmed through, about 3 minutes. Season with extra fish sauce to taste. Sprinkle individual portions with cilantro and peanuts. Serve, passing chile vinegar separately.
