Preheat the oven to 350°F (175°C).
In a large mixing bowl, combine the cooked rice and shredded chicken.
Add the condensed cream of mushroom soup, condensed cream of chicken soup, and sour cream to the bowl. Stir until well combined.
Mix in the chopped onion, chopped celery, chopped green bell pepper, garlic powder, onion powder, dried thyme, salt, black pepper, and milk. Stir until evenly incorporated.
Transfer the mixture to a greased 9×13-inch casserole dish and spread it out evenly.
Sprinkle the shredded cheddar cheese evenly over the top of the casserole mixture.
In a small bowl, combine the melted butter and crushed buttery crackers. Mix until the crumbs are evenly coated.
Sprinkle the cracker topping evenly over the cheese layer.
Bake the casserole in the preheated oven for 40 to 45 minutes, or until the casserole is bubbly and the topping is golden brown.
Remove from the oven and let it cool for 5 minutes before serving.