You quote the introduction to chapter 2: "Kant’s dichotomy between the world apparent to us and some unknowable more really real world beyond is based on and buttressed by his peculiar theory of logic. I refer especially to his analytic-synthetic dichotomy." This was intended to link this chapter with the previous, in which I discussed Kant's fanciful claim to a transcendental reality.
In the conclusion of chapter 2, I wrote: "The logic proposed by Kant does not correspond to the logic of actual human discourse; it is a mere incoherent invention of his. He may have pretentiously called it a critique of pure reason, but I would call it an impure critique devoid of reason. If he describes reason erroneously, he is logically bound to end up with absurdities like the unbridgeable gulf between things-in-themselves and things-as-they-appear. But such difficulties are not the fault of reason; they are the fault of (his own) unreason."
Through that chapter, I describe aspects of how humans actually develop knowledge and show that this method does not correspond to the one erroneously proposed by Kant (notably, the analytic-synthetic dichotomy). The connection between these two chapters is the workings of Kant's own mind - in the same way as he lacks logical acumen in his proposed theory of knowledge, so he lacks intellectual skill in his proposed theory of twofold reality. The same amateur mind is at work, producing both of these silly theories of his.
Still, I would place the analytic-synthetic dichotomy as logically underlying the things-apparent or in-themselves dichotomy, for the following reason. Call these his epistemological and metaphysical claims, roughly speaking. His metaphysical claim is essentially imaginative, whereas his epistemological claim is a more intellectual construct. The metaphysics he proposes is not historically new - all religions have used similar ideas; whereas, his epistemology constitutes a novel attempt to intellectually justify that metaphysics by laying claim to possibilities of a priori knowledge, i.e. knowledge quite independent from experience.
Something about you (optional) logician-philosopher