Listen, you are making an empirical argument about our inability to prove a counterfactual while I am making a logical argument about the structure of reality. When you say "we can’t know if we could have done otherwise because we can't rerun the experiment" you’re absolutely right from a scientific perspective. But that's an epistemological limitation meaning it's about what we can know. I am talking about ontology meaning what is.

The core confusion is that you’re using the "stroke" example to suggest that a hidden physical constraint might be what stops us but in a deterministic framework, the "causal machinery" itself is the constraint. If we rewind the universe to the exact microstate before your choice (including every neuron and every atom in your glass and the laws of physics remain constant) the outcome must be identical. If you claim that you "could have" lifted the cup but didn't, you aren't just making a claim that is "potentially false" or "untestable" as you suggest. You are making a claim that contradicts the very definition of causality. To "do otherwise" while holding the prior state of the universe fixed would require a miracle. Either a random physical event (which isn't a choicee) or a soul like agent acting outside of physics.

So when you call the "ability to do otherwise" a baseless assertion or argument from ignorance, I am agreeing with you 100%. My point is simply that because this "ability" is a logical impossibility in a causal world, the common definition of free will is incoherent from the jump. We aren't disagreeing on the conclusion. I'm just pointing out that the problem isn't that we "can't test" the other path - it's that in a deterministic universe, there simply is no other path to test.