Dry the Instant Pot insert if needed. Set the Instant Pot to Sauté. Add the andouille and cook for 4 to 6 minutes, until browned around the edges. Remove the sausage to a plate. Add oil only if the pot looks dry.
Add the onion, celery, green bell pepper, and red bell pepper. Cook for 4 to 5 minutes, scraping up the browned bits from the sausage.
Add the garlic and cook for about 30 seconds, just until fragrant.
Add the chicken broth and water, scraping the bottom of the pot well.
Add the quick-soaked kidney beans, Cajun seasoning, thyme, smoked paprika, bay leaves, and black pepper. Stir.
Lock the lid and pressure cook on High for 42 minutes.
Let the pressure naturally release for 20 minutes, then release any remaining pressure.
Remove the bay leaves. Check the beans. If they are not fully tender, pressure cook for another 5 to 8 minutes.
Mash about 1 cup of the beans against the side of the pot, or use a potato masher for a few gentle presses. Do not mash the whole pot.
Add the browned sausage back to the pot. Turn Sauté back on and simmer for 8 to 12 minutes, stirring often, until the beans are creamy and thickened.
Stir in butter if using. Taste and add salt as needed.