On South Korea, you might want to consider this chart instead: https://www.macrotrends.net/global-metrics/countries/KOR/sou...
KOR's Fertility rate has been under 1.25 for two decades. It follows then that "stable" population can only be the result of three factors:
1. Pushing the population curve out through longer lives;
2. Immigration;
3. Time-effect offsets of the fertility rate; for instance, if it's the projected fertility rate of females born in a given year, it would take roughly 20-40 years for the fertility rate to have its effect on the population curve.