Let's start with a basic axiom, a line segment is made of unicorns. Now I can build all sorts of unicorn structures that would be logically sound. In a universe that is made of only information, why is this not possible? Every kind of logic should technically exist albeit locally in the order of the size of observable universe so as to make it seem "normal" and "physical" to sentient beings residing in it.

If no logical system is ever consistent and complete, then logic has a sever blindspot in the analysis of the true nature of reality.