I'm not an expert in this field but I think reproducing realistic gravitational interactions seems to require a lot of fiddly set up with heat baths etc.

Gravity doesn't interact, other than to simply set the shape of the spacetime in which particles move.

I think that might oversimplify things, in addition to being a model-laden description. There are empty-space solutions to GR (and indeed many a physicist has found the intuition that there is nothing but empty space appealing, cf geometrodynamics) and in these situations spacetime itself interacts with itself, no particles at all.

In any case, I would say this is a somewhat bold description of what we know about gravity.

You can disprove my statement by naming something gravity does other than add a shape to spacetime, if you want. Saying "I think you're probably wrong, but I just can't say why" is not an argument.

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".

It's also worth pointing out gravitation waves are a thing (have been detected by LaWD or Laser Wave of Gravitation Detector). Does not mean it's not changing the spacetime shape, indeed, these are a type of ripple in spacetime as might occur if Sally Struthers did a jumping jack.

Yes, by "the shape of spacetime" that refers to every specific location in spacetime having a specific shape associated to it. It you want to expand your view out across a range of space and/or time, yes you can see waves, but those waves are still nothing but just waves of variations in "the shape of spacetime". Because we haven't proven the existence of a graviton yet.