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To be unfunny:
The whole idea of a balls hitting each other universe went out the window when we hit the quantum era. We have had to adapt to a reality where matter is somehow a statistical phenomena, and the details are always hidden from us in one way or another. Entanglement is another confusing thing, and its super common - not just some rare phenomena in a lab, it's more of a fact of particle interaction
So our brains are somehow statisical-chemical-electric sugar powered supercomputers that have entangled state. And the brain actually stretches across the body, with various chemistry being produced throughout
In short, nobody has any idea how brains really work, it's way more elaborate than current AI. It's also likely impossible to fully simulate a brain - it would have to BE a brain
There's a separate question about the nature of randomness in the universe, but all we can know is that follows a normal distribution over time. It seems truly random from our point of view. Of course, who's to say if God likes to fudge the numbers a little
Looking past the technobabble...
The implications of quantum mechanics just reframes what it means to not have free will.
In classical physics, given the exact same setup you make the exact same choice every time.
In Quantum mechanics, given the same exact setup, you make the same choice some percentage of the time.
One is you being an automaton while the other is you being a flipped coin. Neither of those really feel like free will.
Except.
We are looking at this through a kind of implied metaphor that the brain is some mechanism, separate from "us" that we are forced to think "through'. That the mechanisms of the brain are somehow distorting or restricting what the underlying self can do.
But there is no deeper "self". We are the brain. We are the chemical cascade bouncing around through the neurons. We are the kinetic billiard balls of classical physics and the probability curves of quantum mechanics. It doesn't matter if the universe is deterministic and we would always have the same response to the same input or if it's statistical and we just have a baked "likelihood" of that response.
The way we respond or the biases that inform that likelihood is still us making a choice, because we are that underlying mechanism. Whether it's deterministic or not it's just an implementation detail of free will, not a counterargument.
Absolutely. And to add to that: quantum mechanics doesn't disproof determinism either. The fact that we use a probabilistic model to some success does not mean the universe has a probabilistic nature. Perhaps the process that determines the outcomes of quantum mechanics is a well behaved random function that can be understood in principle, but is computationally irreducible.