I saw an interesting take on the whole thing suggesting that the US might've been behind this. US military is effectively in control of occupied Korea, so there's no chance that a military backed coup could happen without the US knowing.
So, the question becomes why the US might want to stage a coup in occupied Korea, and the answer may be that the US wants arms sent to Ukraine. The ruling party does not have the majority and they can't authorize arms transfer because the opposition is blocking it. On top of that, the opposition is leaning towards normalizing relations with China, and it's hostile to Japan getting in the way of Asian NATO.
It might be that the US lost patience with Korea and decides to speed things up a bit.