How Big A Problem Is Overpopulation?

In Private Eye issue 1585 I read a letter (titled "Fossil record") which claimed, with reference to climate change:

"The only real answer is the control and reduction of the planet's exploding population. All environmental problems are caused by basically one thing: human overpopulation."

From one perspective that's self-evidently true. However, the "exploding" part is completely misdirected.

The BBC's The Climate Question What role is overpopulation playing in the climate crisis? led me to this quote in Hannah Ritchie's article Global inequalities in CO₂ emissions on Ourworldindata:

"Even several billion additional people in low-income countries - where fertility rates and population growth is already highest - would leave global emissions almost unchanged."

The only real answer, if we want to stay below 1.5°C warming, is a complete and rapid transition away from fossil fuels in the wealthy parts of the world, where population is falling - unless you believe millions in the global North will volunteer for euthanasia in the next few years.