If the ribs have a thin white membrane on the back, remove it by sliding a butter knife underneath to loosen, then grip it with a paper towel and peel it off.
In a small bowl, mix together the paprika, garlic powder, onion powder, chili powder, salt, and pepper. Rub this seasoning blend all over both sides of the ribs.
Pour 1 cup of water into the Instant Pot insert and place the metal trivet inside.
Position the ribs upright on the trivet, with the bones vertical. You can lean the ribs against the sides of the pot. If the rack is halved, it's fine for the pieces to touch. If it’s whole, curve the rack to fit.
Secure the lid and turn the steam release valve to the sealing position. Set the Instant Pot to pressure cook on high for 25 minutes for baby back ribs (use 35 minutes for spare ribs).
Allow the pot about 15 minutes to come to pressure, then the cook time will begin. Once done, let the pressure release naturally for 15 minutes, then carefully turn the steam release valve to venting to release any remaining pressure. (For spare ribs, let the pressure fully release naturally.)
Transfer the cooked ribs to a foil-lined baking sheet. Brush with BBQ sauce and broil in the oven for 3–6 minutes, just until the sauce caramelizes and begins to brown. Watch closely to avoid burning.
Serve the ribs warm with extra BBQ sauce on the side.