Yup, if all countries got to the "1st world countries" birth rates the population would slowly start to drop, maybe even equalize at some point.

Population collapse is like a banking collapse, it happens slowly at first and then all at once.

Well if you don't fix the problem of "it's too dystopian to even think about having children", sure

That’s not the main reason why so many more people are childless now. We have a long road ahead to fix this.

At a global scale yes. Now look at specific countries/continents, some are absolutely exploding: https://en.wikipedia.org/wiki/Demographics_of_Nigeria#/media...

https://www.populationpyramid.net/africa/2020/

They currently use a tiny fraction of the energy the west does (and pollute a tiny fraction), they'll eventually catch up in "quality of life", with all the comes with it (exploding energy consumption)

And they’ll follow the same curve that India did and China before them and so on but I’ll bet the time scale will be greatly compressed because they benefit from all of our experience and technology and having so many more countries ahead of them on the curve who will invest in them.