The emptiness and nothingness of the film is one of the main themes of the film and it achieves this in two ways. The first is to show the vast nothingness in space, and I think Tommy Lee Jones' character alludes to this when he finally meets Brad Pitt. That there really is nothing, and it's all for nothing. That it's all empty and meaningless, and its empty and meaningless
is empty and meaningless (I'll circle back to this later).
The second is meant to mirror the journey we made into South Vietnam in Apocalypse Now (this movie is described by the director as a space Apocalypse Now) . A slow, meandering journey from civilisation into barbarianism (or in this case, a slow meandering journey from population into barren-ness). Where with each passing moment, more and more of what we are used to is stripped back until we're in a more primal state. We see this in the journey Brad Pitt takes alone to Neptune.
So what do we learn from all this...well we see Brad Pitt try and find some hope of a life with meaning...meaning that he imparts. I saw the movie when it first came out so my memory is hazy but I think after he returns back to earth, he reconnects with his ex-wife, and appreciates these things because they mean something to him, even if all there is is nothingness. He, and us as the audience, comes back as a changed man. There's some more ontological and phenomenological themes I remember thinking about when I first saw it, but it's been so long they all escape me. Your post has given me a nudge to maybe watch it again.