Place the chicken in a large saucepan and sprinkle with 1 teaspoon kosher salt; cover with cold water.
Bring to a boil over high heat, then reduce to medium and simmer until the chicken is cooked through and no longer pink, about 12–15 minutes (22–25 minutes if frozen).
Transfer the chicken to a large bowl and shred with two forks.
Discard the poaching liquid, return the shredded chicken to the saucepan, and add the salsa and all seasonings (cumin, garlic powder, onion powder, paprika, chili powder, 1/2 teaspoon kosher salt, and pepper).
Simmer the chicken mixture over medium heat until warmed through, about 3–5 minutes, adding a tablespoon of water if it seems dry.
Remove from heat and stir in the lime zest and juice.
Serve the shredded chicken on warmed tortillas with desired toppings.