Mix celery soup and beef stew seasoning together in a small bowl to create a creamy paste.
Turn on a multi-functional pressure cooker and select Saute function. Add chuck roast and cook until juices start to render and outside is browned, about 5 minutes per side. Add the paste mixture, broth, onion, and mushrooms. Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 40 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Add potatoes and carrots. Close, lock, and return cooker to high pressure. Cook for 15 minutes more.
Release pressure using the natural-release method according to manufacturer's instructions, 10 to 30 minutes. Transfer roast to a large bowl and shred with 2 forks; remove any excess fat. Run remaining liquid through a strainer into a separate bowl. Beat liquid with a whisk until well blended and emulsified, about 1 minute.
Serve shredded roast on top of the vegetables and cover with gravy.