Turn on a multi-functional pressure cooker (such as Instant Pot®) 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.