Wow, very thought provoking!!
I think about this a lot, growing up in a place that controlled your every desire. I think that for one the biggest signs of free will though, is the ability to say no to a desire. As you touched on, desire can be controlled and sometimes are just chemicals reacting in our body, body is craving sugar so it gives you a desire for a cookie. Desire can also be governed by memories, emotional trauma, etc. But the real free will comes in when we can say no, fight back in a sense. This is where choice comes in. Free will gives us a choice to say no to our desires, or yes to them. Depression, ptsd, and many mental illnesses alike, can become a choice if we learn why they happen. Follow me for more on this topic!
Thanks for writing!