Preheat the oven to 400°F. Lightly coat a 9 × 13-inch baking pan with nonstick cooking spray, then place it aside while preparing the casserole mixture.
Remove and discard the skin from the rotisserie chicken. Pull the meat away from the bones, then shred it or cut it into small, bite-size pieces. Set the prepared chicken aside.
Place the chicken in a large mixing bowl. Add the cream of chicken soup, cream of celery soup, and cream of mushroom soup. Stir in the onion powder, garlic powder, black pepper, 1 cup water, 1 cup milk, and 1 cup instant rice. Mix thoroughly until the ingredients are evenly incorporated.
Transfer the chicken and rice mixture to the prepared baking dish. Spread it into an even layer from edge to edge.
Scatter the grated Parmesan cheese evenly over the surface of the casserole.
Bake uncovered for 40–50 minutes, or until the casserole is thoroughly heated, bubbling around the edges, and golden brown across the top.
Remove the dish from the oven and allow it to rest for several minutes before serving.