If this continues, the world population, while still growing due to people living longer, [2] will not grow due to more births anymore. All things being equal, after a while, population would start decreasing.
None of this is necessarily cast in stone: people could start having more children again, or life expectancy could massively drop. But as things are trending right now, population will stabilize relatively soon and then decrease (it's already happening in some countries).
How crowded the Earth needs to be to be considered overpopulated is debatable and a separate question. But if the population does not keep growing there is a path to getting there, assuming the peak population is considered too high.
Of course, that's all the same tech that space habitats would use too, so why not do both?