Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Cook and stir beef and onion until browned, 5 to 10 minutes. Pour in beef consomme, tomatoes, water, and tomato soup. Add carrots, celery, barley, thyme, and bay leaf.
Close and lock the lid. Select Soup function; set timer for 30 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions, about 10 minutes.