Heat the olive oil in a large skillet over medium heat. Add the sausage, onion, garlic, bell peppers, and celery, Sauté for 5 minutes, then transfer to the slow cooker.
In the same skillet, melt the butter. Stir in the flour to form a roux. Cook and stir continuously until deeply caramel colored, about 6–10 minutes. Add the chicken stock a little at a time, whisking until smooth.
Transfer the mixture to the slow cooker, then add the can of tomatoes, Creole seasonings, oregano, bay leaves, thyme, and Worcestershire sauce. Stir to combine.
Add the chicken breasts, making sure they're fully submerged under the liquid.
Cover and cook on high for 3-4 hours or on low for 6-7 hours.
Remove the cooked chicken breasts and shred them with two forks.
Return the shredded chicken to the slow cooker.
Add the shrimp. Cover and cook for 10–15 minutes, until the shrimp are just cooked through.
Skim off any excess fat and season to taste with salt and pepper. Serve warm, garnished with green onions.