There are several competing, and sometimes complementary perspectives on what 'nature' means. Some include humans and their activity within it, others do not.
One thing you can ask yourself: if human activity and the impact it has on its environment is included in what you call 'natural', then what even does remain of the word 'unnatural'? What do people refer to, when they use that word? If you don't have any sensible explanation for it, then the whole thing collapses, yet evidently a lot of people really want to keep using the word nature and even seem to have no problem in making themselves understood when doing so.
That's interesting. Aren't there examples in nature where a species essentially destroys itself? There are many on the population level. Plants often do this, its called succession.
There's a layer to this, where natural also implies good and unnatural implies bad. For example, plastic is bad because it is unnatural, but arguing it is natural after all somehow makes it good (that is the rhetoric I believe). This depends on the notion of a 'natural order', whether that is some vague concept of 'the universe' or of God himself. Anything against that order is bad and unnatural. Humans are part of that order.
Of course, that is very pre-modern idea. I believe what comes close to a useful definition of natural would be something like 'emergent' or 'spontaneous', as opposed to deliberately designed. Its a quality you could also ascribe to, for example, cities or software systems. You don't need the human/nature split for it to be useful. It is not exactly capturing what people think of as natural, but then again we also do not believe in God anymore - by and large. At least not in the way we used to.
One thing you can ask yourself: if human activity and the impact it has on its environment is included in what you call 'natural', then what even does remain of the word 'unnatural'? What do people refer to, when they use that word? If you don't have any sensible explanation for it, then the whole thing collapses, yet evidently a lot of people really want to keep using the word nature and even seem to have no problem in making themselves understood when doing so.