For us, we avoid any added butter/lard/oils but a nut like walnuts can be processed until a nut butter, or at least chopped finely. This would replace some of the fats.
For a crumble, much like granola, mixing oats and apple sauce (or pear sauce or any cooked down fruit), and nuts, will essentially be a topping.
If you make it wet, it will be soggy, if you make it moist, it will be both chewy and crumbly, if you make it dry it will be crumbly. That texture changes somewhat connected to the baking apples in it, and then it will also change when you store it.
So ideally we make it moist, eat it right after baking for chewy and crispy. At least have the expectation it will become less crispy when you store it.