Press the Sauté button on the Instant Pot® and melt butter. Add onion and cook until softened, about 3 minutes. Add poblano and Anaheim peppers, tomatillos, and jalapeños and cook 3 minutes, then add garlic and cumin and cook until fragrant, about 30 seconds. Press the Cancel button.
Add chicken thighs, stock, and water to pot. Close lid, set steam release to Sealing, press the Chili button, and cook for the default time of 30 minutes.
When the timer beeps, quick-release the pressure, open lid, and stir well. Press the Cancel button and remove chicken to a cutting board. Carefully remove skin from chicken and shred meat with two forks.
Use an immersion blender to purée sauce until smooth. Stir meat, cilantro, and beans into sauce. Serve warm.