Free will centers around the subjective experience of making a decision. Deterministic or not, my mind is making a selection from a limited number of choices. When people question whether or not a deterministic mind could be considered to be making choices, what they are usually really asking about is culpability. When something bad happens, the first question is, “Who is responsible?”
The implication here is that if I am deterministic I cannot be held accountable. Firstly, this view misses the point of punishment, which is to alter the payout for unwanted behavior, which works no matter the mechanism behind the decision-making process. The fact that your misbehavior can be traced back to prior causes is not only obvious - anything less is impossible.
At the end of the day, it’s a question of evaluating your judgment. Did you make a good decision or not? People who balk at the idea of a deterministic human mind might do so because the automatons we are all familiar with are so obviously incapable of exercising any judgment, good or bad. Soon though, we will be contending with the subjective decisions of machines in the same way we do with other (human) strangers in daily life.
The question of how much one can push another before their decision becomes yours is one reason legal representation is so darn expensive these days.
Free will is much better conceptualized as meaning free from outside interference. Even if the ultimate underpinnings of our minds are mechanistic, as long as we can “freely choose” between options without coercion, then it is fair to consider us the cause of the outcome of whatever decision we make.
But what does it mean to “freely choose” if we are deterministic? It means we are aware and present in the scenario with the options being presented, we can conceive of the possible outcomes these entail, and we select one of them. Challenges to culpability tend to focus on defending against one of these points. If all of these conditions are true, then yes, you are the reason that event occurred, deterministic or not.
None of this changes what it feels like to make that decision though. Making decisions is all about reasoning under uncertainty. We only ever have partial information, and we’re making our best guess about what’s going to happen next. That tension between uncertain futures, all balanced on your fingertip, is what free will is getting at.
"Free will is the subjective experience of making a decision"
That's not the generally accepted definition. The problem of free will starts with the feeling of free will, but it's only a problem is to explain whether there is a real ability behind the feeling.