1. I don't think unpredictability is a great definition of free will. Its incomplete imo.

2. The compatiblist definition seems what ur closest too, and this seems like a reasonable free will. Most philosophers believe in compatibalist free will.

3. Libertarian free will is absolute nonsense on par with believing in fairies and only a thought in peoples heads because of religious indoctrination. This requires being able to do different if you hit replay... as you correctly state is nonsense.

Redefinitions of free will are kind of useless imo... as ur simply not talking about what others are. Theres way too much baggage on the term free will causing equivocation on redefinition. Whats the point of redefining free will to some infinite state space predictability stuff that has nothing to do with what others mean... why not use a different term to define a different concept? I think the reason is because we piggyback off the baggage of the term "free will".

Theres issues with scale of predictability as well. Example quantum systems and reality may be fundamentally probabilistic, but for any actual mental decisions and things at human scale they fundamentally aren't probabilistic and are predictable. Similarly unpredictable numerous potential neuron states does not mean unpredictable decisions or actions. Also human action is fundamentally highly highly predictable in many ways, our inability to predict things does not mean they are unpredictable. I guarantee when ai can better measure brain states it can certainly predict our outcomes almost perfectly. As neural nets will make this trivial.

If ur definition relies so heavily on predictability, what happens to your "free will" when ai or a psychologist predict your behavior. Do mentally ill people or people with bipolar have more free will because their actions are fundamentally more unpredictable?

I think there is also massive problems with ur infinite state space claims. Taking the amount of neurons then just adding them as a binary is insanely wrong... thats not how neurons work even remotely, or math, or brains, or physical space. Its akin to saying theres 2^^999999999999999 atom combinations in my body... therefore i have infinite potential of body forms i can take. Its preposterous imo. Theres also assumptions like every neuron can interact, despite that obviously not being even close to true as neurons can only interact with the few in their proximity. Also theres the issue of equating mental representations of physical numbers to a binary brain state, as if our understanding of the number 1 = brain state neural binary 01.. this is not what numbers or how our brain represents them. Then there is the issue of even if i grant all this... that immeasurably large number of neuron combinations is still not infinite... its unreachable... BUT its fundamentally NOT infinite.

Maybe i just don't understand what you mean... but then again thats another problem with redefining words with a lot of baggage.