Preheat the oven to 450 degrees F (230 degrees C).
Place mushrooms, red bell pepper, and onion in a baking dish.
Thread chicken pieces onto skewers that are about the length of the short end of the baking dish.
Mix olive oil, tamari, apple cider vinegar, Worcestershire sauce, paprika, ginger, and stevia in a small bowl. Add 1/3 of the sauce to the mushroom mixture, stirring to coat.
Place chicken skewers across the pan of vegetables. Brush about 1/3 of the sauce on top using a basting brush. Cover chicken on both sides, allowing sauce to drip onto the vegetables.
Bake in the preheated oven for 10 minutes. Leave the oven on and transfer skewers to a plate. Stir the vegetables; place skewers back on top and baste chicken with the remaining sauce. Sprinkle poultry seasoning on top.
Continue baking in the hot oven until vegetables are tender and chicken pieces are no longer pink in the centers, about 15 minutes more.