As a South Korean currently living in the US, let me add my perspective:
1. North Korea ceased to be an "existential threat" to South Korea a very long time ago. According to Wikipedia, South Korea's GDP is 1.4466 trillion USD; North Korea's is estimated to be 25 billion USD. That's a factor of 58.
For comparison, USA's GDP is 17.95 trillion USD. Cuba's is 77.15 billion USD. That's a factor of 233.
So, see how much Americans feel threatened by Castro these days, and multiply that by four.
2. The only way they could be a major threat is if they go suicidal. However, they are not ISIS: Kim Jong Un has no intention of becoming a martyr. (Of course, he has a lot to gain by looking like a crazy, unstable dictator who could start a war any day: North Korea is the master of this mode of "crazy diplomacy".)
However, in the extremely unlikely case that Kim decides to go full nuclear, ironically, all these nuclear missiles would make little difference to South Korea. North Korea has millions of soldiers and enough conventional weapons to burn Seoul down to ground. Adding one Hiroshima-size nuke or two will be... well, like adding one Hiroshima to the whole Pacific War, I guess.
This makes about half of South Koreans go "meh" at the news of yet another nuclear test. They can already kill us, and if they do, they will be killed, too. Everybody knows that. Nothing has changed.
Of course, America does not like having such a "rogue" nation with a nuclear missile that can hit San Francisco, so all this posturing is basically targeted advertisement for the US. I think they are saying, "Look at me, we have nukes now, so you will be sorry if you attack us!" They're trying to cut some kind of deal with the US. (Of course it may actually provoke US into some "preemptive strike," so it's a very risky gambit, for them and also for the whole East Asia. But when did they ever care for human lives anyway?)