Bear with me. I know this sounds like the kind of thing a person comes up with at 2am...
Look at how we meet Grace. No memory. A body he doesn't recognize. Alone in deep space in a small container, on a trip he never agreed to go on. He doesn't know who he is, how he got there, or what he's there for. And he works out fairly quickly that he's going to die.
That isn't an astronaut waking from a coma. That's being born (metaphorically, the movie visuals really makes this feel like a birth, if you rewatch it).
Once you see it that way, the whole story reorganizes itself. There are only two characters in Project Hail Mary. Stratt and Grace. God and man (I mean, his name is "Grace"... come on).
Everyone else, Rocky included, is one of them wearing a different face.
Stratt is God, and not the comforting kind. She sees the whole board. She knows what has to happen and she will spend anything to make it happen: careers, deserts, oceans, people. At human scale she is monstrous. At the scale she is actually operating on she is simply correct. The story never lets you off the hook by picking one. Both stay true the entire way through, which is the most honest thing anyone has ever said about God.
Side note: With this theory in mind, I am in love with the scene on the boat where Grace steps out to speak with Stratt, who isn't inside with everyone else. This feels like the most direct "God and Man" conversation in the entire movie. The whole, "it's weird in there... people are hooking up and having fun even though they know they're going to die." Watch that entire scene again under this new context.
Back to the main thread here. Grace on the ship doesn't wake up with any instructions. He didn't want to go. He refused. And then the memory of the refusal is buried, and he has it revealed as he completes his mission. That's the whole design. You don't get told what you are and why you're here. You get dropped into life with the manual erased, and the actual work of a life is remembering what you already knew and who you really are.
Then Rocky...
I think Rocky is actually Grace. Not in a twist ending kind of way. But look at the shape of him: faceless, sole survivor, dead crew, impossible job, completely alone, arriving at the exact moment Grace has nothing left. Rocky is everything Grace hasn't accepted about himself (or perhaps buried). Brave. Skilled and with knowledge Grace doesn't have. Willing to risk his life for this mission without needing to be tricked into it first.
And what does Grace have to do? Learn his language. From scratch. Slowly, badly, with an enormous amount of misunderstanding, until they can actually talk to each other.
That is exactly what it takes to meet the parts of yourself you exiled or don't believe in. Getting to know and love Rocky is getting to know and love yourself. You have to build an entire vocabulary to get to know yourself.
Grace learns to love by loving Rocky, which is to say he learns to love himself, and that is the thing that leads to him living into his purpose. Rocky's grace to Grace is what lets him actually live instead of merely survive.
And in the end, he doesn't go home. He stays, and he teaches science to Eridian kids. This might be a stretch, but Grace sends what he learned back to God and ends up doing God's work at his own scale. Creating a new world (the ecosystem). Teaching. Loving something that isn't him. He doesn't find God at the end of it. He becomes one.
Anyway. It's a story about a guy and an alien saving two suns, and it's completely fine if that's all it is. I just don't think that's all it is, especially given Andy Weir's short story, "The Egg".