Trim excess fat from chicken; season both sides with salt, pepper, garlic powder, and onion powder.
Set Instant Pot to Sauté. Add olive oil and brown chicken 2–3 minutes per side. Press Cancel.
Pour in chicken broth and scrape up all browned bits from the bottom of the pot.
Pour BBQ sauce, Worcestershire sauce, and honey over the chicken without stirring it into the broth below.
Lock the lid, set valve to Sealing, and pressure cook on High: 10 minutes for breasts, 15 minutes for thighs.
Natural release 5–10 minutes, then quick-release remaining pressure.
Shred the chicken in the pot with two forks and stir to coat in sauce.
Optional: Sauté 3–5 minutes to thicken the sauce. Serve on buns, over rice, or with your favorite sides.