In Instant Pot, add stock, onions, chicken, brown sugar, chili powder, paprika, garlic powder, onion powder, mustard, salt and BBQ sauce in that order. No need to mix.
Close lid and turn vent to "sealing." Set Instant Pot to "manual" on high pressure and set for 10 minutes. Allow it to naturally release.
Shred chicken and add more BBQ sauce if desired.
Notes
Add stock first so it helps avoid the burn notice you might get otherwise in the Instant Pot.
If you like heat, add some crushed red pepper flakes.
To quickly shred the chicken, use an electric hand mixer. It goes by much faster.