A lot of population specialists have challenged the UN figures and consider them to be too high and that peak population will be around 2050.
With nearly half of all countries having already reached the point where their birthrate is below replacement rate and another swathe very close to that point, I think the evidence favours those who consider the UN estimates too high.
I still believe that by the end of this century population figures will be stable or falling and by the end of the next century will have fallen significantly. To quote the UN itself Between 2019 and 2050, populations are projected to decrease by one per cent or more in 55 countries or areas, of which 26 may see a reduction of at least ten per cent. In China, for example, the population is projected to decrease by 31.4 million, or around 2.2 per cent, between 2019 and 2050.