Nature has value because we exist. It wasn't as important to us for a while (and still isn't) but hopefully in the future it will become more and more important to people.

Nature also has value in that it is almost irreplaceable. If humans are around long enough that we see our entire planet destroyed, we live in space; in order to replace/get a new "nature" it would take billions of years of waiting and exactly the right conditions, which may not even be reproduceable.

And even then you get a different nature; if we want the same ecosystem we have now, then it is truly priceless, truly irreplaceable.

Agreed. Nature without humans has no value. Nature has value because humans value it.

And at the same time humans are a part of nature. When the first humans built a hut out of wood and leaves that isn't different than a beaver building a dam.

The idea that the only "true nature" is that which has not seen human activities makes no sense. Same with the logic that "we can only heal nature by removing humans".