Should I count water from food?
Yes, at least conceptually. Food can contribute meaningful fluid, especially fruit, vegetables, soups, yogurt, cooked grains, potatoes, and many mixed meals. You do not usually need to log food-water precisely, but it explains why two people with the same beverage intake can have different hydration status.
This also explains why hydration can feel different when you change diets. Moving from restaurant food and mixed meals to lean protein, dry grains, and low-sodium whole foods may reduce water and sodium intake unless you deliberately replace them.