Let me see if I got your point, and if we may even agree in some points, Witt.
The physiological basis of the cognitive processes (including free will) is extremely complex and far from completely understood.
However, the basic component of such process is necessarily the neuronal activity, which in its most basic expression can indeed be decribed as a categorical response (YES or NO), as you rightly stated.
Therefore (as I conceded many posts ago) AI should im principle be able to express free will. Again, far as I'm aware that is still not the case.
And again, that is entirely irrelevant for our debate. In fact, if AI would be ever able to express free will, then the latter must necessarily exist.
Cause is not antonym of option. The same cause (stimulus) can provoke many different responses in humans.
Even more; causation does not contradict either consciousness or intentionality, neither in principle nor in ´practice.
It seems your argumentation on determinism and causation goes far beyond cognition (free will included).
Utter determinism would in fact negate chance; no event would be truly aleatory in the Universe, from the Big Bang onwards and even before. Am I right?