Turn on a multi-functional pressure cooker (such as Instant Pot(R)) and select the Saute function. Add oil. Sprinkle Italian seasoning over chicken breasts and add to the hot oil. Cook chicken until browned, about 2 minutes per side. Turn the pot off. Pour in chicken broth.
Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 10 minutes. Allow 5 minutes for pressure to build.
Release pressure using the quick release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Transfer chicken to a serving plate. Drain the pot.
Select the Saute function again and add Italian sausage. Cook and crumble sausage into small pieces, about 2 minutes. Add bell pepper, mushrooms, and onion. Cook until sausage is brown, about 2 minutes. Add pizza sauce and olives. Cook for 4 minutes, stirring continually.
Spoon sauce over chicken on the serving plate and top with mozzarella cheese.
