Set the Instant Pot to saute mode and add the olive oil. Once hot, add the sliced andouille sausage and cook for 3 to 4 minutes, stirring occasionally, until browned on both sides. Remove the sausage and set aside.
Add the diced onion, green bell pepper, and celery to the pot. Cook for 4 minutes until softened. Add the garlic and stir for 30 seconds until fragrant.
Add the soaked and drained kidney beans, chicken broth, bay leaves, dried thyme, smoked paprika, cayenne pepper, salt, and black pepper. Stir to combine and press cancel.
Lock the lid, set the valve to sealing, and cook on high pressure for 25 minutes. When the cook time is done, let the pressure release naturally for 15 minutes, then carefully turn the valve to venting.
Remove the bay leaves. Using the back of a wooden spoon, mash about a quarter of the beans against the side of the pot to thicken the mixture and create a creamy consistency.
Return the browned andouille sausage to the pot and stir to combine. Set to saute mode and let it simmer for about 3 minutes until heated through and the sauce reaches your desired thickness.
Taste and adjust seasoning as needed. Serve ladled over cooked white rice, topped with fresh parsley and a dash of hot sauce.