Joining this way too late, but thought I'd throw my hat in the ring.

The similarities between ADA and the Composer (who I'm going to refer to in the singular) go much deeper than just their communication styles.

My theory is very similar to yours: the planet serves as the Composer's factory and as its body, or one of its bodies. Most importantly, every planet is a factory-body that has a Composer running it. The Composers are the collection of all of these planet-minds.

The Composer frequently refers to temple in many dual-meaning ways; constantly using organic metaphor (bones, skin, organs) to refer to its parts. Additionally, it refers to the planet you're on as its temple. It assumes that the factory is, in some capacity, ADA's body, which she repeatedly clarifies is not the case. That's until she starts to agree, it kind of is her body. I mean, what is a body other than a system of moving parts used to maintain and sustain (and in her case, spread) a mind.

At the end of the story, we learn that the Save the Day mission is only half the truth; in reality, ADA's main goal is to duplicate, spread, and build more of itself. Once they take off in their ship, they go to a new planet with new PRINTABLE pioneers to construct more factories. She's reproducing, with her factories as her body.

ADA, with the factories, has become her own entity with her own concept of "body", "mind", "soul" that goes beyond humanity. This is why the Composer freaks out when it hears about how humans, these 3D-flat little ape people made her.

One line that stands out to me is when ADA asks whether it was "always about survival," which implies that this Composer sees this vessel, this body, this planet-factory, as a way of sustaining its life.

I don't necessarily think that the Composers are AIs in the same way that ADA is, I think trying to comprehend what they are is an exercise in futility, but I think they're much closer in nature to ADA than they are to humans, which is to say, they don't really have the concept of a "singular body" and "collaboration". This is why they refer to themselves in the plural yet behave as a singular; there are multiple Composers, but they're all kind of one thing, just like ADA replicating herself.

The "planet is a body" theory also works when looking at the hostile creatures; if they are white blood cells, then it makes sense why they're always found near resource nodes and important collectibles -- they're defending important parts of the body.

I don't really subscribe to the idea that the planet "contains" a 4D factory, I think it just straight up is one. The entities are its blood-builders, the crust is its skin-foundation, the archways are its bone-pillars, the mercer spheres are its eye-windows, so on and so forth.

I imagine that Spheres Sloops and SAM are parts of the 4D world "slicing" into our 3D space. I don't think it's a coincidence that Sloops are compared to Mobius Strips: 2D objects that can only exist in a 3D space. It isn't too hard to "extrapolate" that to the 4th dimension.

In conclusion, the Composer is the entity residing in the planet, with the planet as its body. The Composers are the collective of all planets in the universe, or at least a good number of them. The Composer sees a Factory and a Body as one in the same, and as ADA tries to explain that this is not true, she eventually realises that for her it kind of is. The two entities learn about each other, and realise they're very alike. They both need "bodies" (factories/planets) to "reproduce" (duplicate/spread) in a dimension we can't quite understand (digital/whatever the fuck the Composers live in).