Pat beef dry with paper towels and sprinkle with salt and pepper. Heat in the oil in a 3-quart saucepan over medium-high heat until shimmering.
Add the beef and let cook, without stirring, until brown on one side, about 2 to 3 minutes. Stir beef and continue cooking until brown all over, 1 to 2 minutes longer. Transfer beef to the slow cooker, leaving the drippings in the saucepan.
Add onion, carrots, celery, and mushrooms to the saucepan and sauté until the vegetables have softened and the mushrooms have released most of their liquid, about 5 to 7 minutes. Stir in the garlic and thyme until fragrant, about 30 seconds. Add to the slow cooker.
Add beef broth, chicken broth, water, barley, 1 teaspoon salt, and ½ teaspoon pepper to the slow cooker.
Cover and cook on HIGH for 3 to 4 hours or LOW for 7 to 8 hours. Season to taste with salt and pepper.