Bring 6 cups water to a boil. Stir in 3⁄4 cup salt and sugar until dissolved. Add sage sprigs, thyme, and bay leaves. Pour salt mixture into a clean 5-gallon bucket or pot. Add 18 cups cold water; let cool. Add turkey to brine; refrigerate overnight.
Meanwhile, make the dressing: Heat 2 tbsp. oil in a 4-qt. pot over medium- high heat. Add half the Vidalia onions; cook, stirring, until soft, 8–10 minutes. Stir in rices, add wine, and cook until reduced by half, 3–4 minutes. Add stock, bring to a boil, reduce heat to low; cook, covered, until rice is tender, 40–45 minutes. Spread rice on an oiled rimmed baking sheet; let cool slightly.
Heat oven to 425°. Cook bacon in a 12" skillet over medium-high heat until crisp, 10–12 minutes. Transfer bacon to paper towels; return skillet to medium heat. Add remaining Vidalia onions and garlic; cook, stirring, until soft, about 7 minutes. Add oysters and 1⁄4 cup of their juices; cook for 1 minute.
Transfer oyster mixture to a large bowl along with rice, bacon, bread, half the butter, the minced fresh sage, and hazelnuts. Season with salt and pepper; mix. Grease a 9" x 13" baking dish with 1 tbsp. butter; mound dressing in baking dish. Dot dressing with remaining butter; cover with foil and bake for 40 minutes. Refrigerate dressing.
Reduce oven to 350°. Drain turkey and pat dry. Season lightly with salt and pepper; rub with remaining oil. Stuff cavity with celery and onions; tie ends of legs together with kitchen twine. Set turkey, breast side down, on rack inside a roasting pan. Roast turkey for 1 1⁄2 hours. Using paper towels, turn turkey breast side up; cook until an instant-read thermometer inserted into the deepest part of the thigh reads 160°, about 2 hours more. Let rest for 20 minutes.
While turkey is resting, raise oven heat to 475°. Remove dressing from refrigerator, uncover, and bake until browned, 20–30 minutes. Carve turkey and serve with dressing.