I'm not trying to disprove what you are saying, I'm just providing some context. Although, point of fact, I think its a weird framing, since even GR, which you seem to be talking about, casts gravity as reciprocal with matter. As the old saying goes: spacetime tells matter how to move, matter tells spacetime how to bend. If that isn't an interaction, I don't know what is.
But, that aside, the idea that gravity is spacetime is really just the theory of general relativity and that is clearly not the final word on the subject. Other approaches to gravity may admit alternative ontologies.
Again, I'm not trying to prove or disprove anything. Just saying that you are kind of oversimplifying an open scientific question.
Shape of space simply means the "Metric Tensor", and saying it's the sum total of what General Relativity is describing isn't some "bold" or "weird" framing (your words); it's both complete and correct.
It isn't so simple, even in GR:
https://plato.stanford.edu/entries/spacetime-holearg/
Thanks for the link. I'm not even saying GR isn't emergent from something else. All I'm saying is that it contains the sum total of what is currently the proven mathematics governing gravity.
I myself have many 'unproven' things about Physics, that I believe, with a high degree of probability (near certainty). Dig thru my past posts for lots of them. For example, I believe Minkowski Space is indeed itself emergent. I think our entire universe exists on the "surface" of a 3D Event Horizon (manifold). I don't believe in the Big Bang, because our reality 'formed' not from a singularity (exploding out), but like a Black Hole (falling in). So I'm open to lots of ideas, but just pointing out the what we currently know as General Relativity, isn't even that complex, and is just about a shape (curvature/tensor) at every point in spacetime. It's all we've "proven".