So we have
Perhaps these observations put us in a position to see some problems with the questions asked in the OP.
This phrase ought to give us pause. We have seen that we cannot step outside our representations of the world. If that is so, then there can be no “structure of reality itself”, but only a structure within some representation.
Given that we can choose from amongst many logics, yes, it is a tool, used to model how things are. Logic governs validity, forming a grammar in which we can talk coherently about how things are. Our ontology is not entirely fixed, but not just any model will do. Some inferences will be invalid.
Really? What work does that word do here? We cannot step outside of our representations in order to achieve a “really”. What we can look for is coherence and agreement in our representations. They are far from arbitrary.
Those who cannot abide having a choice of logics sometimes insist that one true logic was handed down by god. It’s a pretty poor position. If nothing else, it seems to place undue limits on what god is capable of.
Our logic and language are inherently part of the world; which is to say again that the world is what imposes constraints on our words - but more, on what we can and cannot do. What we say about the world is part of what we do in the world. One way or another, it is enacted.
Why does a Philips head fit so well into a Philips screw? Not just because of design, but because the one makes no sense without the other. We can only do what is available to us to do. The very idea of an unconceptualised structure is incoherent. What looks like a map is also the territory.
All of the above is pretentious shit, of course. It’s what we do that is important.