Set the Instant Pot to Sauté. Cook the andouille for 3–5 minutes until lightly browned. Remove to a bowl, leaving the rendered fat behind.
Sauté the onion, bell peppers, and celery for 4–6 minutes until softened. Add the garlic and cook 30 seconds until fragrant. Stir in the chipotles, adobo sauce, paprika, oregano, and bay leaves; cook 30 seconds.
Add the drained beans, chicken broth, and salt. Scrape the bottom thoroughly to release any browned bits.
Pressure cook on High for 15 minutes. Allow a natural release for 15 minutes.
Check bean tenderness. If not fully creamy, pressure cook an additional 5 minutes (quick release is fine).
Stir in the rice. If the beans are loose and brothy, add rice plus ½ cup water. If thick, add rice plus 1 cup water.
Pressure cook on High for 4 minutes. Natural release for 15 minutes.
Taste and adjust salt. Fluff gently and rest 2–3 minutes before serving.