Instant Pot® Pulled Pork

Name: Instant Pot® Pulled Pork
Ingredients: 0.25 cup brown sugar; 1 tablespoon chili powder; 1 tablespoon paprika; 2 teaspoons garlic powder; 2 teaspoons kosher salt; 1 teaspoon ground black pepper; 1 teaspoon cayenne pepper; 1 (4 pound) pork shoulder roast, trimmed, or more as desired; 2 teaspoons olive oil; 1 cup chicken stock; 2 cups water; 1/3 cup apple cider vinegar; 2 tablespoons brown sugar; 1 (6 ounce) can tomato paste, divided; 1 large sweet onion, quartered, or more to taste; 0.5 cup ketchup, divided; 0.5 cup brown sugar