Place the beef in a medium bowl. Add the salt, black pepper, and flour, then toss until evenly coated.
Select the Sauté setting on the Instant Pot and heat the olive oil. Add the beef and cook until browned on all sides, about 5 minutes. Work in batches if necessary to avoid crowding the pot, transferring browned beef to a plate.
Add the onion, garlic, carrots, and celery. Cook, stirring frequently, for about 5 minutes, until the onion begins to soften. Stir in the oregano, basil, and tomato paste.
Add chopped onion, garlic, carrots and celery. Continue to cook and stir for another 5 minutes.
Pour in 1 cup of the hot water. Scrape the bottom thoroughly with a wooden spoon or spatula to loosen all browned bits.
Return any reserved beef and its juices to the pot. Add the remaining 1 cup water, beef broth, and pearl barley. Stir to combine. Keep the contents below your appliance’s half full limit as the food will expand.
Cancel the Sauté setting. Secure the lid and set the valve to Sealing. Select Pressure Cook on high pressure for 15 minutes.
Allow the pressure to release naturally for 10-15 minutes then release the remaining pressure manually. Once all the pressure is released, carefully open the lid, keeping your face away from the steam.
Stir the soup and check that the beef and barley are tender. If needed, simmer on Sauté, stirring occasionally, until tender.
Add a little extra broth if you prefer a thinner soup. Taste and adjust the salt and pepper before serving.