Season chicken with paprika, garlic powder, salt, and black pepper. Combine chicken breast and 2 cups stock in an electric pressure cooker (such as Instant Pot®). Close and lock the lid. Turn on the pressure cooker and select Stew function. Set timer for 25 minutes. Allow time for pressure to build, 5 to 10 minutes.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Transfer chicken to a cutting board. Set pressure cooker to Saute function and allow broth to come to a boil. Shred chicken meat using 2 forks.
Add frozen dumpling wrappers to the broth, stirring often to prevent sticking together. Add shredded chicken, cream of chicken soup, and remaining stock to the pressure cooker. Add salt and pepper to taste. Close and lock the lid and set pressure cooker to Stew function. Set timer for 10 minutes. Allow time for pressure to build, 5 to 10 minutes.
Release pressure using the natural-release method according to manufacturer's instructions, 10 to 40 minutes. Unlock lid; stir in peas and carrots and allow to sit until warmed through, 1 to 2 minutes.