Turn Instant Pot or pressure cooker to sauté function. Add oil and sauté onion and garlic until softened. Add vinegar, ketchup, relish, mustard, Worcestershire sauce, molasses, and hot sauce. Stir frequently.
Cook mixture and reduce down to more of a paste-like sauce, approximately 3-5 minutes.
Season chicken thighs with salt and pepper. Add chicken to Instant Pot and mix in with the sauce. Replace and lock the lid. Set the release valve to sealing and pressure cook the chicken for 15 minutes.
When complete, use the quick release method and turn valve to venting and allow steam to escape for a couple minutes. Then remove the chicken and transfer to a rimmed baking sheet.
Press the sauté function again on the Instant Pot and sauté the sauce to thicken it, about 8-10 minutes.
Meanwhile, shred the chicken. Add some sauce to shredded chicken and mix together.
Serve with additional sauce if desired.