Exercise has some huge physiological and psychological benefits [0]. It won’t immediately cure serious mental illnesses, but it definitely doesn’t hurt.
Anecdotally, my mental health is much better with a good diet and some physical exercise every week.
That’s true of diets, not exercise. Physical exercise is always measurable and always works. Whether you can do the exercise is another matter. It should be tailored to your body. It should be hard. It should hurt (in soreness, not in pain). I’ve seen people transform.