Turn on a multi-functional pressure cooker (such as Instant Pot(R)) and select Saute function. Add oil, onion, and bell pepper and cook until slightly softened, 3 to 5 minutes. Turn off Saute function and add jackfruit in a single layer on top of vegetables.
Whisk tomato sauce, brown sugar, mustard, tomato paste, Worcestershire sauce, sriracha sauce, vinegar, garlic powder, parsley, salt, and pepper together in a bowl. Pour this mixture evenly over jackfruit in the pressure cooker. Close and lock the lid; choose the Slow Cook option and set the timer for 4 hours.
Toast hamburger buns and serve topped with cooked jackfruit.
