You've raised a big question. I've written many articles on our relation to nature. Just a few of them are linked below.
Metaphysically we're natural rather than supernatural. But historically, psychologically, socially, and culturally, we're anti-natural. The driving force of cultural progress--which could be leading to our extinction--is Promethean or Luciferian, to put it in figurative terms. When we shifted from egalitarian, nomadic bands of hunter-gatherers into sedentary, hierarchical civilizations, we locked ourselves into a path that put us at odds with nature in so far as nature is the inhuman wilderness.
I'm not opposed to thinking we're part of a greater good, but the Nietzschean question is whether there's a viable such good after the death of God or the collapse of Christendom and the modern humiliation of Western religions. What is the best hypermodern faith?
It's easy to say we should be spiritual in seeing how we're part of nature. But look around at all the ways we're manifestly opposed to nature; look at how our artificial environments destroy the ecosystems, and how we seek refuge from the wild in humanized worlds that cater to our whims and reassure us that we're still important, even if the grosser anthropocentric myths of theistic religions have been undermined.
To say that spirituality has been misunderstood is an understatement. Christendom has bastardized spirituality, inverting what I'd prefer to call our challenge to be authentic in the existential sense.