Set Instant Pot to "saute" at high heat. Add the oil then brown the ribs on all sides--you may have to do this in batches. Since these ribs are long, I generally cut them in half so they're easy to handle. Remove to a plate and drain any accumulated fat, leaving about a teaspoon in the pot.
Fry the onion and mushrooms on the saute setting at medium heat until onions are soft and mushrooms begin to sear. Then deglaze the pot with the wine, scraping up any browned bits. Add the water and onion soup mix; stir well.
Add the ribs back to the pot and cook at high pressure for 40 minutes. Release the pressure as soon as the time is up.
Remove the ribs, set the pot to saute at medium heat and whisk in the mushroom soup. If you desire a thicker sauce, mix the flour with the 1/4 cup water and stir into sauce. Let the sauce cook for 5 minutes then place the ribs back in the pot to heat through.