Actually this is not really the case. While the birth rate is extremely low, Korea‘s current elderly population is only 15%, that‘s lower than the US at 16%, UK at 18%, and Japan is already at massive 28%. Korea‘s average age is also younger and they have more than 2x the immigration rate of Japan, 5% of the population are foreigners compared to 2.3% in Japan. It will take decades before Korea even reaches most of Europe‘s current levels and they will never reach Japan‘s situation as the population will start to decline before that.

Current projections have the 65+ population peaking at 19% in 2050, so while the population will fall, Korea is not falling into the same trap as Japan or Germany. https://www.statista.com/statistics/712843/south-korea-population-projections-by-age-group/

Meanwhile Japans current projections are almost 39% of the population to be 65+ by 2040. https://www.statista.com/statistics/607936/japan-forecast-population-age-group/

The economies are also just vastly different. Korea is a low debt and high export economy, debt is only 50% and export volume is double per capita of Japan. Japan meanwhile is carrying a huge 200%+ debt on a more domestic consumption focused economy with much more protectionism and less export.

The chance of Korea slowing down anytime soon is basically slim to none, at least not for another 10 years.