Combine flour, Italian seasoning, onion powder, salt, and pepper in a gallon-sized resealable plastic bag. Shake to mix seasoning. Add beef to bag, seal, and shake to coat.
Select Sear function on a multi-functional electric pressure cooker (such as Instant Pot) according to manufacturer's instructions. Add coated beef cubes and sear until lightly browned on all sides, 7 to 10 minutes. Pour in broth and red wine. Add tomato paste and garlic. Stir in potatoes, onion, carrots, celery, rosemary, and bay leaf.
Close and lock the lid. Select Stew setting and set timer for 25 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions, 10 to 40 minutes.
Meanwhile, fill a large pot with lightly salted water and bring to a rapid boil. Cook egg noodles at a boil until tender yet firm to the bite, 7 to 9 minutes. Serve alongside beef stew.