My guess is that South Korea probably only will become directly involved if the US does, and frankly, if the US becomes directly involved, I think that Russia's going to either fold or play nuclear hardball, either of which kind of shuffles expanded conventional conflict out of the picture.
Russia has absolutely zero chance against the United States in a conventional war. so you're right, that they'll either capitulate, or destroy the world.
Beyond troops, it could also open up Ukraine to South Korea's arms market. South Korea makes a ton of artillery pieces that it doesn't sell on the international market. Becoming a cobelligerent with Ukraine could change that.
They also make this thing, which would be GREAT in the Ukrainian theatre, seeing as it’s only a few tons heavier than a T-90, but chock full of essentially current NATO-spec equipment. Also, Poland signed a deal for an absolute SHITLOAD of them (~1000 iirc - yes, a thousand), with local production options, so this would not only be an incredible way to get actual battlefield testing done with them, but also give the Korean arms industry a major cred boost. Not to mention, I would be unsurprised if Ukraine eventually figures out a joint production deal with South Korea, especially if the tanks perform well.
Oooh oooh I have bets that SK loosens restrictions on what they will export and can start power pumping out 155mm shells for Ukraine to squash their northern foe.
They've already kinda been doing that, just indirectly. Western partners have been giving their old stock of 155 to Ukraine and then resupplying with Korean made 155s.
I think a real game changer would be if they actually decided to give them access to the K2 tank. It would be interesting to see what an actual modern tank could do in Ukraine, especially considering they have layers of protection against drones and atgm. Plus they can crank them off the production line faster than any other nation.
Is the k2 actually designed for constant combat? Ukraine seemed to really struggle with the abrams, but that's designed to have equal or greater maintenance time to fighting time.