Preheat the oven to 325°F.
Scatter the bread on a baking sheet, season with herbes de Provence, and toast in the oven until golden, 10 to 12 minutes. Set aside.
In a large nonstick skillet, heat 1 tablespoon oil over medium-high heat. Add sausage and cook until fat renders, about 2 minutes. Add chicken and cook for 3 minutes, then add shrimp and cook until pink and firm, 3 to 4 minutes. Season with salt and pepper; set aside.
In a second skillet, heat the remaining 1 tablespoon oil over medium-high heat. Add bell pepper onion, garlic, and celery, season with salt and pepper, and cook until tender, 7 minutes.
Add reserved bread cubes and veggies to the sausage mixture and toss to combine; set the veggie skillet aside. Stir in 1 cup chicken broth and lower the heat to low.
In the veggie skillet, melt the butter over medium heat. Whisk in the flour and cook for 1 minute. Whisk in the remaining 2 cups chicken broth and the hot sauce, season with salt and pepper, and cook until the gravy is thickened, 1 to 2 minutes.
Pile the stuffing into bowls and top with the gravy, scallions, and thyme.