Heat oil in a multi-functional pressure cooker (such as Instant Pot) on Sauté mode. Add beef and onion; cook until beef is no longer pink on the outside, about 4 minutes. Add green beans, celery, carrot, garlic, oregano, dried basil, and black pepper to the Pot; stir to combine.
Add broth, diced tomatoes, and crushed tomatoes to the Pot; stir to combine. Select Soup setting; close and lock the lid. Select High pressure according to manufacturer's instructions; set timer for 35 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Stir in kidney beans and pasta. Turn on Slow Cook mode; cook according manufacturer's instructions until vegetables and pasta are tender, about 10 minutes. Season with salt. Top servings with Parmesan cheese and fresh basil.
