Set the Instant Pot to the 'Sauté' mode. Add olive oil to the pot. Once hot, add the diced onion and cook until it becomes translucent, about 3-4 minutes.
Stir in the minced garlic and diced bell pepper. Sauté for another 2 minutes until fragrant.
Add the canned diced tomatoes (with juice), shredded jackfruit, black beans, kidney beans, vegetable broth, chili powder, cumin, smoked paprika, oregano, salt, and pepper. Mix well to combine all ingredients.
Seal the Instant Pot lid, ensuring the valve is in the sealing position. Set to 'Manual' or 'Pressure Cook' on high for 15 minutes.
Once the cooking time is complete, allow for natural pressure release for 10 minutes before manually releasing any remaining pressure.
Open the lid, stir the chili, and taste for seasoning. Adjust salt and pepper if needed.
Serve hot, garnishing with fresh cilantro or slices of avocado if desired.