Load the slow cooker: Spray a large slow cooker with nonstick spray. Add the celery, carrots, onion, chicken broth, both condensed soups, the uncooked chicken, and the poultry seasoning. Stir just enough to break up the condensed soup.
Cook until tender: Cover and cook on LOW for 4 to 6 hours or on HIGH for 2 to 3 hours, until the chicken shreds easily and the vegetables are tender.
Shred and season: Remove the chicken, shred it with two forks, and return it to the pot. Taste and season generously with salt and pepper, adding more poultry seasoning if needed.
Cut and coat the biscuits: Cut each biscuit round into 8 bite-sized pieces. Place them in a large bowl or gallon-size zip-top bag, add the cornmeal, and toss until every piece is coated.
Add the dumplings: Turn the slow cooker to HIGH. Scatter the biscuit pieces over the surface, cover, and cook about 1 more hour, until a toothpick inserted into the center of a dumpling comes out clean. Do not stir during this hour.
Stir and serve: Once the dumplings are cooked through, stir gently. Ladle into bowls and garnish with fresh herbs.