Combine the onion, tomatoes, chiles, beans, stock, chili powder, cumin, and 1½ teaspoons salt in the Instant Pot® and stir to mix. Nestle the chicken pieces into the stock mixture.
Lock the lid in place and turn the valve to Sealing. Press the Pressure Cook button and set the cook time for 20 minutes at high pressure.
Let the steam release naturally for 10 minutes, then turn the valve to Venting to quick-release any residual steam. Using two forks, shred the chicken into bite-size pieces. Add the lime zest and half of the lime juice. Taste and adjust the seasoning with more lime juice and salt if needed.
Ladle the stew into bowls and layer with toppings as desired. Serve with lime wedges alongside.