Make sure the liner is in the Instant Pot, then press the saute button to turn on. Add the olive oil and butter.
Add the flour, onion powder, salt, and pepper to a large mixing bowl. Whisk together to combine. Add the stew meat to the bowl, tossing to coat evenly.
Remove the coated meat from the bowl, and shake off any excess coating then add the meat and onions to the hot oil and butter in the pot. Sautee them for 5-7 minutes, stirring occasionally.
Add both the broth and water to the pot to deglaze, and use a sturdy wooden spoon to scrape up any stuck on browned bits.
Add the onion soup mix and bay leaves, stirring to combine. Dump both cans of tomatoes and tomato sauce in, but DO NOT stir.
Hit the cancel button to turn off saute mode. Add the lid and turn to close. Turn the vent valve to the sealed position, a cook on manual for 30 minutes. Let the pressure naturally release for 10 minutes, then carefully open the vent valve to release the remaining steam.
Open the pot and remove & discard the bay leaves. Remove the beef & tomatoes from the pot using a slotted spoon, and transfer it to a bowl. Use the back of the wooden spoon to lightly smash the tomatoes against the sides of the bowl to break them up some. Set aside.
Add the carrots and potatoes to the pot, stirring to combine. Close the lid, set the vent valve to seal and pressure cook on manual for 7 more minutes. Carefully open the vent valve and release the hot steam.
Cook the egg noodles according to the package instructions until al dente. Drain.
Return the beef & tomatoes to the soup, and add the corn. Stir to combine.
Add a scoop of noodles to a bowl, and ladle soup over top. Serve warm & enjoy!