Combine soup, water, chicken, celery, onion, salt, poultry seasoning, and pepper in a large, heavy pot. Cover and cook over low heat for 1 1/2 hours.

Add potatoes and carrots; cover and cook for another 30 minutes.

Remove chicken from pot, shred it, and return to pot. Add peas and cook only 5 minutes longer.

Add dumplings. To make dumplings: Mix baking mix and milk until a soft dough forms. Drop by tablespoonfuls onto boiling stew. Simmer covered for 10 minutes, then uncover and simmer an additional 10 minutes.