Season chicken all over with salt and pepper; add to pot. Cook, turning over halfway through, just until exterior of chicken is opaque, about 2 minutes total. Add sage, thyme, 1 Tbsp. Diamond Crystal or 1¾ tsp. Morton kosher salt, and 1 quart water. Bring to a boil, then reduce heat and simmer, uncovered, until chicken is tender and cooked through, 30–35 minutes. Discard sage and thyme. Using tongs, transfer chicken to a plate; let cool slightly, then shred meat with 2 forks.