Pat the chicken thighs and shrimp dry with paper towels and season both lightly with a pinch of salt and black pepper.
Set the Instant Pot to Sauté on high and add the olive oil and butter to the pot, allowing the butter to melt completely.
Add the sliced andouille sausage to the pot and cook, stirring occasionally, until browned and some fat has rendered, then transfer the sausage to a plate and leave the drippings in the pot.
Add the seasoned chicken pieces to the pot and sear until lightly browned on the outside without fully cooking through, then transfer the chicken to the plate with the sausage.
Add the diced onion and both bell peppers to the pot and sauté, stirring often, until softened and beginning to caramelize, then stir in the minced garlic and cook until fragrant.
Stir in the diced tomatoes, chicken broth, tomato paste, Worcestershire sauce, smoked paprika, dried thyme, garlic powder, onion powder, salt, black pepper, cayenne pepper, and bay leaves, scraping the bottom of the pot well to release any browned bits.
Return the browned sausage and chicken along with any accumulated juices to the Instant Pot and stir to distribute everything evenly in the cooking liquid.
Cancel the Sauté function, secure the lid on the Instant Pot, set the valve to Sealing, and cook on Manual or Pressure Cook high pressure for 8 minutes.
While the jambalaya cooks, heat a large skillet over medium heat, add the olive oil for the cauliflower rice, then add the riced cauliflower and cook, stirring often, until tender and just beginning to turn golden in spots.
Season the cauliflower rice with the salt and black pepper and continue cooking until any excess moisture evaporates and the texture is fluffy rather than wet, then remove from heat and set aside.
When the Instant Pot cooking time is complete, allow the pressure to release naturally for 5 minutes, then carefully perform a quick release to vent any remaining steam and remove the lid.
Turn the Instant Pot back to Sauté on low, discard the bay leaves, and gently stir in the raw shrimp, simmering until the shrimp are opaque and just cooked through.
Taste the jambalaya and adjust the seasoning with additional salt, black pepper, or cayenne pepper as desired to balance the flavors and heat level.
Add the cooked cauliflower rice directly to the Instant Pot and fold it gently into the jambalaya until the cauliflower is evenly coated with the sauce and warmed through.
Let the jambalaya sit on the Warm setting for a few minutes to allow the cauliflower rice to absorb some of the flavorful juices and to slightly thicken the mixture.
Serve the keto Instant Pot jambalaya hot, topped with chopped green onions and fresh parsley, and garnish each bowl with extra cayenne or hot sauce if you like more heat.