I don’t think there is a way to have the categories and latest topics view on mobile due to screen real estate restrictions.
That screenshot of your mobile view is for a not logged in user, which means they are always going to see all the pinned topics at the top because in that state, Discourse doesn’t know whether or not they have read them. It will look different if you view it logged in.
Do you still have an issue to solve if you are logged in?