https://carnegieendowment.org/2022/08/15/south-korea-s-decap... provides this account of official ROK strategy:

> Every Pyongyang district, particularly where the North Korean leadership is possibly hidden, will be completely destroyed by ballistic missiles and high-explosive shells as soon as the North shows any signs of using a nuclear weapon.

For the DPRK the official strategy is not known as far as I know, but in 2022 they passed a new law explicitly authorising preventive nuclear strikes if "it is judged" that ROK is going to strike state leadership. See https://www.apln.network/analysis/commentaries/north-koreas-... which also links to a janky translation of the law.