The question of whether we enjoy autonomous, libertarian free will or only experience the illusion of same is unanswerable. The universes that contain one would be indistinguishable to us from those containing the other.
Libertarian free will is the idea that the will is not the result of anything other than the conscious self itself, which is its author unaffected by external reality including the brain. That is, in libertarian free will, the will originates in the conscious mind, whereas with the illusion of free will, the self receives instruction from the brain to the mind, and wills what it does passively while mistaking itself as the origin of that will rather than a passive conduit for it. It implies that in the exact same circumstances, one could will either of two (or more) things - an undecidable question. You can't reproduce those exact circumstances ever again to test it, and even if you could go back in time to the moment when you chose A and make a choice again, even if you chose B, you still wouldn't have an answer, because you wouldn't know that you had been in that moment before - if you did, then it's not the exact same reality - or that you were doing a test, or how it turned out before.
Furthermore, the answer would be useless even if we had it. What would you do differently if you knew one were the case rather than the other? Some say that punishing immoral behavior is itself immoral if there is no libertarian free will, but humanists hold that view in both cases. Punishment is not a part that thinking. That's a religious idea and central to Christianity, for example, since punishment is the reason given in biblical myths for why bad things to happen to humanity under the rule of a tri-omni deity. Humanism rejects punishment - inflicting gratuitous suffering - as is described in hell. It rejects the idea of prisons inflicting suffering beyond what confinement necessarily entails. Confinement is not to punish, but to serve as a disincentive to lawbreaking by the convict and others who see what becomes of scofflaws, and to remove a danger from the streets.
Some say that believing that will is not free is permission to or cause to behave differently. That wasn't the case for me. I suspect that free will is illusion, but I haven't always. Between then and now, when I went from assuming that I had libertarian free will to a place where I seriously question that, I had a period of cognitive dissonance as I assimilated that, but in the end, nothing changed. I still behave as if my will originated with the subject of consciousness even though I know that that is likely to be incorrect, because it doesn't matter either way.
I don't see where anything useful can be added to any of that. We don't know, we can't know, and knowing wouldn't be helpful even if we did know.