Prepare shredded chicken using your preferred method (Instant Pot, crock pot, or stovetop). For Instant Pot: combine chicken thighs, diced onion, 15-oz can green enchilada sauce, 1 cup green salsa or chicken broth, diced green chiles, and sea salt in the Instant Pot and stir.
Secure the Instant Pot lid and pressure cook on High for 20 minutes, then allow natural release for at least 10 minutes (up to 1 hour if convenient). Use quick release for any remaining pressure. If using another method, cook until chicken is fully cooked and tender.
Use tongs to transfer the cooked chicken to a cutting board and shred with two forks.
Return the shredded chicken to the cooking liquid and mix to moisten; reserve about 1/2 cup of the sauce for the casserole base.
Preheat the oven to 400°F (200°C) and spread the reserved 1/2 cup of sauce in the bottom of a 13x9-inch casserole dish. If leftover chicken has no sauce, use canned green enchilada sauce or salsa, or spray the dish with cooking spray.
Dip each flour tortilla briefly into the shredded chicken mixture to soften and absorb some sauce, then place about a heaping 1/2 cup of shredded chicken in the center and roll tightly into a taquito shape. Repeat to make 8 enchiladas.
Arrange the rolled enchiladas seam-side down and tightly packed in the prepared casserole dish.
Pour or spread the remaining green salsa (1 to 2 cups, depending on desired sauciness) evenly over the enchiladas.
Sprinkle the grated jack cheese evenly over the top and bake for about 20 minutes, until the sauce is bubbly and the cheese is melted and lightly golden.
Remove from oven, sprinkle with chopped green onions, cotija cheese, and fresh cilantro if desired, then serve.