In a large nonstick skillet, heat the olive oil over medium-high heat. Add ground turkey and cook for 5 minutes, using a spatula to crumble the meat. Add the mushrooms and cook for 3 minutes, stirring frequently, until the turkey is no longer pink and the mushrooms have begun to soften. Add salt, chili powder, garlic, and ginger, and stir to combine. Add the soy sauce mixture to the pan and stir to coat all ingredients. Cook for 3 minutes to allow the sauce to thicken slightly. Add carrots, scallions, and water chestnuts, and give the whole pan one final stir. Remove from heat.