We've outpaced genetics alone long ago, using our brains and dexterity to hunt, make fire, create clothing for most of the world's biomes, sail across the seas, etc. It's a sort of cultural evolution that continued where genetic selection slowed down. You can see lighter versions of that in animals, like chimp tribal cultures, raven sub groups (and language "dialects"), learned tool use passed down across generations in otters, etc.
But semantics aside, if our population grows faster than we can adapt, well, either we catch up (with better medicine, food, shelter, economics, agriculture, distribution, climate mitigations, etc.) or people start dying. Usually the poorer people in developing countries.
It's incredibly difficult to model human population collapse because there's so many more unknowns with us than other, more predictable species. If a supervolcano goes off and we suddenly face a global crop failure and massive food shortages, maybe the remaining countries will all try to work together to work out a new production and distribution system like we did with COVID. Or maybe the rich countries will start hogging all the resources, like we also did with COVID. If Putin nukes Europe tomorrow, that would change things, or if some high schooler gets fusion to net positive energy in her friend's garage, a lot of things would get easier. If ChatGPT goes Skynet on us next year, maybe we'll be all killed, or eaten, or saved. Who knows.
In the meantime, most countries don't have population control programs (the way China did a few decades ago) so people keep popping them out, especially in areas with either high poverty (needing child labor) or high infant mortality (gotta make a bunch in case a few die young). On the other hand birth rates are slowing down, or already negative, in many developed economies because a lot of people have trouble affording kids (in time or money), for example, or don't want to bring them into this world. I guess there's some hopelessly slim chance of a Star Trek style "fully automated luxury space communism" future, but more likely you'll have a few rich powerful people and everyone else working for pittances, with people dying left and right but enough getting made to replace them in the commodity labor market. We already have most of that system in place today.
And nature? An afterthought, until it isn't, at which point the survivors will adapt anew and we'll go through similar boom and bust cycles again and again... yay, the circle of life and all that.