Begin by setting your Instant Pot to the sauté function and adding the canola oil. Once the oil is hot, add the chopped onion, garlic, red and green bell peppers, and celery. Sauté for about 5 minutes, or until the vegetables are softened and fragrant.
Next, add in the chicken chunks and sliced andouille sausage. Stir well to combine and cook for an additional 5-7 minutes until the chicken is lightly browned and the sausage is heated through.
Sprinkle in the Creole seasoning, cayenne pepper, thyme, rosemary, oregano, and a bit of salt and pepper. Stir the mixture well, allowing the spices to coat the meats and vegetables for about 1 minute.
Pour in the chicken broth, canned diced tomatoes (with their juices), liquid smoke, and Worcestershire sauce. Then, add the rice and bay leaves. Stir gently to combine, ensuring the rice is submerged in the liquid.
Close the Instant Pot lid, making sure the valve is set to sealing. Set it to manual high pressure for 8 minutes. Once the cooking time is up, let it naturally release pressure for 10 minutes, then carefully switch to quick release to release any remaining steam.
After the pressure is fully released, open the lid and gently fold in the thawed shrimp. Close the lid for another 5 minutes to allow the shrimp to cook through with the residual heat.
Remove the bay leaves and taste for seasoning. Adjust with more salt, pepper, or cayenne if desired. Serve hot, garnished with fresh parsley or green onions if you like.