Yes, but also no. In a very literal sense, human beings are animals, and our modification of the world is technically the same kind of thing as, like, a bird building a nest. But I think there is some utility in distinguishing between human activities and non-human activities. We are uniquely capable of altering the environment in ways that no other creature can.

Not sure if we are on the same page.

While managing woods, etc. has some validity, we do it for us to be more convenient. Infestations due to dead wood and forest fires do have their natural order.

And "humans being separate from nature": We do like to create our ideal environments, like beavers. Be it due to us having next to no fur or it being a widespread trait in mammals, who knows. But humans affecting every ecosystem with their machines and being everywhere should either not do that (like some tribes) or not being everywhere.