I came close to abandoning this question for it seemed just another version of: "Do objective facts exist?", "Is there non-empirical knowledge? and so on. But trying to express my meaning of "structure", I realized all examples had one thing in common: the human mind. Then realized that any non-human-mind related (objective?) structures I manage to communicate would actually be subjectively imposed. (So maybe now I truly get what "A-thing-in-itself" is?)
But we're talking about structure, not things. And immediately I hear "Structures can be described and studied, hence they are knowledge also." However I submit that this is like English being its own meta-language, and that these are human-mind constructions. Mostly, we cannot assume there is similar relations between objective knowledge and structure as there is between our own constructs.
Edit: As pointed out by Conifold, thus far we just have a faint echo of Kant. Now as I understand Kant's "categories of experience" they are structural phenomena, we situate facts, or objects of knowledge, in frameworks such as dichotomy or a formal system, for example. It must be noted that the focus inquiry can be these frameworks themselves such as in programs like Structuralism. However we always find that (at least as far as human pursuits are concerned) there are "things" that may be termed "data" and some sort of frame of reference, or structure, within which they can be made sense of.
Kant rightly realized that we cannot arbitrarily extend these experiential reference frames. Our understanding is limited by the scope of our perceptive history. However the present question is wondering whether there are some meta-structural knowledge, maybe something about the relationship between data and data structures, that may be gleaned from our experience based knowledge and extended to the metaphysical. (In some sense this is a rehash of my earlier question about gaining knowledge that would hold inside and out outside a simulation.)
Question: Are there any philosophers who have studied the (possible) metaphysical difference between knowledge objects and objective structures?
Where "objective structures" are structural entities that exist independent of human experience, like how many would see Mathematics or Logic. And "knowledge objects" are things existing without a need for observation, like how physicalists sees most of the universe.