One thing that's not being realised is that many countries' populations will keep growing due to the inertia of previous growth. The EU fertility rate is about 1.5 children per woman over her lifetime, which should in theory be a recipe for decline.
But because of previous population growth in the 1960s/70s/80s/90s there are far more women in their 20s and 30s having babies than there are women in their 40s-60s becoming grandparents, who are in turn a larger cohort than the great grandparent generation who make up most of the people dying. Every single country in the world has got this baked in population growth, so even South Korea, with a fertility rate of less than one, can still see organic population growth in the short term due to the cohort in their twenties and thirties being so large relative to the cohort born in the 1940s and 50s.
But once you get one generation further on the tide will turn and it will turn quite suddenly. Nobody has found a way of making well educated women with good access to contraception want to have more than 2 children on average. Not Sweden, not Denmark, not France (who give huge tax breaks).
And in the wider long term view that's a good thing, because the world can't take 8 billion people with the lifestyles that they all aspire to, but it will take a lot of management. We have decades of warning that this is coming - we need to use it wisely.