Turn on a multi-functional pressure cooker (such as Instant Pot) and select Saute function. Heat olive oil and cook ground beef, ground pork, and onion until meat is crumbly and onions are soft and translucent, about 5 minutes. Stir in garlic. Turn off Saute function and drain grease.

Season with brown sugar, Worcestershire sauce, apple cider vinegar, paprika, salt, pepper, and bay leaves. Mix in beef broth, cabbage, tomato sauce, diced tomatoes, and rice. Close and lock the lid. Select high pressure according to manufacturer’s instructions; set timer for 15 minutes. Allow 10 to 15 minutes for pressure to build.

Release pressure using the natural-release method according to manufacturer’s instructions, about 15 minutes. Unlock and remove the lid. Stir soup and serve.