To be clear: I'm far from an expert in the topic, so all I can provide is a shrug and some possible factors to consider.

One is that as much doom and gloom has been spread about Japan's socio-economic situation since the 90s, the country continued to stumble along as the world's second-turned-third largest economy. Certain problems (both economic and demographic-related) continue to persist if not worsen in Japan, but so far they haven't caused the ceiling to collapse so to speak; perhaps this indicates that these kinds of decay are much slower and lead to a gradual erosion rather than a catastrophic downfall so often implied by the media. In other words, "just keep kicking the can down the road" seems to keep these types of issues somewhat at bay for decades. So one conclusion is to look at Japan and say "clearly this type of thing isn't sustainable in the very long term, but countries can continue lumbering along even under these pressures."

However, as mentioned initially, the problems in South Korea sound way worse than in Japan: the birth rate is much lower, the cost of living much higher (IIRC), the pressure on youth to follow a specific path to success is more intense, etc. For instance, I don't remember anyone in Japan ever reported saying "my spouse and I are just having one kid so that we can put all of our time, money, and focus into preparing them for their academic and job-search success" (I don't know how prevalent an attitude this is in SK today, but I've heard it does exist). Plus there are other factors, like SK has a much smaller population, economy, and global reputation than Japan (in the '80s people in the West legit thought Japan was going to take over the world; the bubble years were bonkers like that). In other words, if SK's starting situation is worse than Japan's, and the severity of their problems worse than Japan's, they may not be able to accomplish a similar slow erosion.

Furthermore, the global situation is looking really bad. Without going into too many details (because that would be a post of its own), there are a LOT of economic and demographic and climate factors that are looking really unsustainable in a lot of countries, from housing and general cost-of-living to aging populations and infrastructure to increased instances of severe natural disasters and poor agricultural yields. Back in the Great Recession the saying I heard in Japan was: "the US sneezes and all the world catches a cold." And indeed, Japan got hit pretty hard by the Great Recession, I believe especially so because of their export-oriented economy. So what happens when not just the US, but Canada, Australia, the UK, and many European countries all seem to simultaneously be making the same scrunched-up pre-sneeze face? Meanwhile many other major economies like India are dealing with different but significant looming socio-economic issues (I am really not an expert in Central Asia, but the bits I hear about don't sound good). And then there's China, which from any angle looks like a ticking time bomb IMO. Put it all together, and it's a lot harder to experience slow erosion when the rest of the world is engulfed in a landslide.

Granted, I'm assuming that SK has and will continue to have a similar political culture to Japan, one dominated by the older generations and conservatives/moderates who are more likely to embrace status quo and half-measures than radical reforms. I'm also assuming a similar social culture, one that's not open to possible stop-gap solutions like mass immigration (although given they share the same language barrier issue as Japan, I'm not sure immigration really is the golden ticket everyone makes it out to be regardless). I think these general assumptions are fair as SK is probably the closest country to Japan in terms of cultural similarity, however SK has shown they've a bit more spice to their step (see: massive protests in recent years). Plus the 2020s have become an era of upheaval, and it can be easier to enact radical shifts in trajectory during unstable times.

In conclusion SK is not doomed, but I think they'll need to do more than Japan has simply to obtain a similar slow decline, and they'd need to pull out some near-miracle moves to get back on a healthy track.