Kim Jong-un is not head of state since the DPRK doesn't have one. He is not a government administrator at all. He is the chairman of the WPK party and head of the military. That means he oversees two responsibilities:
1. Reunification through the gradual joining of the two states into a mutual national confederation
2. The defense of socialism in Korea so that unification, independence, and a better future for Koreans may continue to exist.
2. The defense of socialism in Korea so that unification, independence, and a better future for Koreans may continue to exist.
The pursuit of joint reunification of North and South on equal terms has been DPRK policy for so long that the treatise was written literally by Kim Il-Sung https://www.korea-dpr.com/lib/201.pdf
This is all public knowledge. Westerners like to make this way more complicated than it is bc it serves racist imperial ends to mystify a modern socialist republic.
Supreme Leader as a position just means the head of the State Affairs Commission, the means by which the DPRK government is checked and balanced by the vanguard party. All Marxist-Leninist states have some function for party and state to interact, that's the point.
Some Korean comrades have said that Chairman of the SAC can qualify as a head of state since it is a kind of executive body so I'll cede the first sentence. It is not a singularly powerful position however since it's policies are ultimately decided on by the party apparatus.
Kim Jong-Un chairs that party apparatus, but that power is far more distributed at every level.