Select SAUTÉ setting on a programmable pressure multicooker (such as Instant Pot). (Time, instructions, and settings may vary according to cooker brand or model.) Select HIGH temperature setting, and allow to preheat 5 to 8 minutes. Add oil, and stir in smoked sausage. Cook sausage, stirring often, until browned, about 5 minutes. Remove with a slotted spoon, and set aside. Add chicken to cooker, and sprinkle with 1/2 teaspoon of the Cajun seasoning. Cook, stirring often, until browned, about 5 minutes. Remove chicken with a slotted spoon, and set aside.

Add onion, celery, green bell pepper, and red bell pepper to cooker, and cook, stirring occasionally, until vegetables begin to soften, about 4 minutes. Add garlic, and cook, stirring constantly, 1 minute.

Add broth, diced tomatoes, rice, bay leaves, thyme, sausage, chicken, and remaining 2 teaspoons Cajun seasoning, stirring well to combine ingredients.

Press CANCEL on multicooker. Cover cooker with lid, and lock in place. Turn steam release handle to SEALING position. Select MANUAL/PRESSURE COOK setting. Select HIGH pressure for 7 minutes. (It will take 10 to 15 minutes to come up to pressure before cooking begins.)

Meanwhile, toss together shrimp, smoked paprika, salt, and black pepper in a medium bowl. Set aside.

When cooking has stopped, carefully turn steam release handle to VENTING position, and let steam fully escape (float valve will drop). This will take 3 to 4 minutes. Remove lid from cooker, and stir in shrimp. Return lid to cooker, and let stand until shrimp are pink and have cooked through, 8 to 10 minutes. Stir in parsley. Garnish with scallions.