I never understand what people are asking when they debate free will. It's a brain's process. Everybody's got one. Your brain's process isn't necessarily lovely to you, and doesn't necessarily do what you (the brain process) admire, like, or prefer. It's subject to outside influence and isn't perfectly under it's own control, because it's a cranky machine and goes wrong a lot. Some parts of it conflict with other parts. It's slow, and bad at monitoring itself. What do expect, magic? It's still yours, however unfair it may be to be stuck with it. So you have free will, whoopee.
If consciousness (and choices, the output of consciousness) is completely determined by the brain's physical process, then there is no such thing as "libertarian free will" which is what people typically mean when they say "free will".
Metaphysical libertarianism. Yeah, by definition, that's not compatible with the view that everything is determined by physical processes. This is just people freaking out over determinism. I kind of see why. "I am a physical process" sounds like "I am controlled by fate and my choices are pointless". But a person is a process that can't see the future, and a process that experiments and discovers things. Choices are the deterministic process: the person determines things. I could repeat this several times in different words but I'd just be trying to placate a kind of paranoia that happens when people realise they're physical.
Why are you framing this in terms of placating my paranoia? I have no objection to my lack of free will, it does not bother me. It makes me more empathetic to recognize that others lack it as well.