The root of sentience is sense. I would define it as the state of having subjective experience, or qualia. The experience may be external (sense perceptions) or internal (thoughts, emotions). It may be illusory; I would argue, for instance, that one is sentient while dreaming. It may be mistaken: I thought I heard you say “X” when you really said “Y.” It may be distracted: you missed your turnoff because your attention was focused on the audiobook you were listening to. Surely you wouldn’t claim you weren’t experiencing your surroundings for five minutes.

I do take your point about the unreliable narrator, the part of our brain (or perhaps more precisely our mind) that integrates the incoming sense perceptions into a model or narrative of what’s going on around us. This is why dreams are irrational: because the perceptions are being generated internally, by random neuron firings in the brain, rather than originating in the outside world, they are not consistent in the way external reality is. The internal interpreter, struggling to make sense of the inconsistent data, comes up with a nonsensical narrative to explain them. But none of this implies that sentient experience doesn’t exist, or (while awake) has no connection to the Ding an sich out there.

As for determinism and free will, better minds than mine have yet to come up with a satisfactory answer.