Sauté Ingredients: Set the Instant Pot to "Sauté" mode on More or High. Melt the butter, then add diced onion and cook until translucent (about 2–3 minutes). Stir in the sausage and sauté for another 2–3 minutes.
Add Base Ingredients: Pour in the broth, then add one can of white beans (including the liquid), tomato sauce, and bay leaves. Stir to combine.
Pressure Cook: Secure the lid, turn the valve to the "Sealing" position, and set the Instant Pot to Manual or Pressure Cook on High for 4 minutes. While the soup is cooking, drain and rinse the second and third cans of white beans. Set aside. Once cooking is complete, perform a quick release and remove the bay leaves.
Reserve Sausage & Beans: Using a slotted spoon, remove 2½ cups of the sausage, onion, and bean mixture and set aside for garnish.
Add Cheese & Seasonings: Stir in the shredded cheese, maple syrup, liquid smoke, and the second can of drained white beans.
Blend & Final Ingredients: Use an immersion blender (or work in batches with a countertop blender) to puree the soup to a smooth consistency. Stir in the stewed tomatoes, the third can of drained white beans, and the optional red kidney beans.
Serve & Garnish: Ladle the soup into bowls and top with the reserved sausage, onion, and bean mixture. Garnish with additional shredded cheese, if desired.