We can linguistically analyse "free will" to explain what the most common interpretations of the term are, but we'll always miss something.

There are two completely different problems we can try to solve.

The first problem is, "what do people mean by the words 'free will', and what do they believe about the concept they reference, and why do they use these words or concepts to begin with"? This is a problem for linguists, anthropologists, historians, psychologists, neurologists, maybe even evolutionary biologists. And it's a completely empirical one, even if hard to solve.

Crucially, it doesn't seem to be a problem in need of philosophy, unless philosophers are somehow selected or self-selected so that their own self-reports are more valuable than those of other people, while still being representative of people in general. (Nobody really wants to know the answer to "'what do philosophers use the words 'free will' to mean, which is completely unrelated to what everyone else uses those words to mean?")

I hope everyone would agree that whatever people mean by words, and believe about their referent, doesn't necessarily prove any objective truths about the referent.

The second problem we can try to solve is whether there actually is free will and how it should be best described. Of course, if different people mean different things by "free will", then this is a set of different and unrelated problems. Since we're presumably motivated by actual problem(s) and not by the mere occurrence of these words - even if the problems are driven by intuition and not by empirical evidence - we should be able to taboo the words "free will" and state the problems directly. Solving the second kind of problem should not require first solving the first one.

Have philosophers done this? Did they turn out to be working on the same questions? Do they have any good arguments for any of their positions beyond intuitions (which should be used to solve the first kind of question, not the second one)?

ETA: for example, a dualist might say: "spirits can affect matter, creating material effects that don't have detectable material causes. This action is called the free will of the spirit, particularly a human spirit." This might be a strawman which no-one actually believes, but it would be a concrete statement about free will, trying to solve the second kind of problem.

Of course, everything I've said here about free will is applicable to any philosophical debate where not everyone agrees about the meaning of the words being debated.