By the time William is king, George will probably be over 18 and in the position to be both a regent and a counsellor of state. It is also likely that Catherine may be made a counsellor of state by King William V, just as Prince Philip is today. As of today BTW, while Queen Elizabeth II is still alive, both Prince Charles and Prince William would have to be unavailable for Harry to become a regent and there are at least three counsellors of state who would normally take precedence over him (Philip, Charles and William). Furthermore, I also suspect that, if needed, the Queen would be more inclined to assign official state tasks to Andrew, who is also a counsellor of state, than to Harry.
So I mantain what I said and now repeat: Harry will not normally have access to government papers or government ministers , nor will he be routinely involved in state affairs. Let us not fool ourselves into pretending otherwise.