Set the Instant Pot to Sauté. Add the butter, melting it gently.
Pour in the bone broth, then mix in the cream cheese, celery, crab, Old Bay, cayenne pepper, black pepper, salt, bell peppers, whipping cream, onion, and tomatoes. Close the lid, set the pressure release to Sealing, and select Manual/Pressure Cook. Set the Instant Pot to 3 minutes on low pressure and let cook.
When cooking is complete, perform a quick release by carefully switching the pressure valve to Venting. For a smoother soup, briefly use an immersion blender, until desired consistency is reached.