Place chicken in a Dutch oven and add water just to cover. Add onion, celery, garlic, 2 1/2 teaspoons salt and pepper. Bring to a boil, cover, and reduce heat to a simmer. Cook, covered, for 1 hour 15 minutes.
Transfer chicken to a cutting board and let rest until cool enough to handle. Shred chicken and set aside. Discard bones and skin.
Strain chicken broth and set aside. Optional, chop celery and onion and reserve with chicken.
Wipe any debris from the pot or lightly rinse the pot if desired. Return pot to stove over medium-high heat and add butter to melt. Add sausage and cook until well browned. Pour reserved chicken broth and remaining salt into the pot and bring to a boil. Stir in rice and reserved chicken and return to a simmer. Stir once, reduce heat, cover and simmer until rice is tender and most of the liquid has been absorbed, about 20 minutes. Turn off the heat and let stand, covered, for 5 to 10 minutes.
Serve topped with green onions, additional black pepper, and sliced okra if desired.
