I don't know the whole of the compatibilism arguments but they're just defining a moral framework within which you're still accountable. It doesn't say that free will is real.

It can all be broken down as follows:

Rewind time by a certain amount where the entire universe is exactly as it was at that instant. Start the replay. Do you make all the exact same choices, is the universe exactly the same when we get back to the present time?

If the answer is yes, then most people will accept that rejects the most common understanding of free will.

If the answer is no, then by what mechanism were different choices made? How did the neurons in your brain fire differently to make different choices? It must be random. And if it is just random, then that, to me (and many others) also rejects the most common understanding of free will.

But, that doesn't reject the idea of accountability within this system, because accountability is the feedback that directs the neurons to fire in a certain manner to make choices that soiciety prefers. If there was no accountability, no punishment for behaviour that was harmful to other individuals, it would not have good outcomes. So the system creates accountability. It must, because that accountability is part of the physical process by which choices are made.

That’s operating at a higher level. I’m talking about base level fundamental reality.

I fully acknowledge that we feel like we have free will and that we should act like we have it. But it’s still an illusion.

It's not an illusion any more than Vegas odds are an illusion. Free will is the (correct) perception by an agent that its actions can't be predicted by other agents. My guess is that there will never be an agent that can predict my moment-by-moment thoughts and actions, so I'll always have free will.

No, that definition is arbitrary.

Free will is the idea that there is a "you" and you are the author of your actions, or at least you can significantly influence your actions.

Of course, your actions are authored by the neurons in your brain but most people speak as if there is more to it than that. As if there is a "you" that exists outside the brain.

If you can imagine, say, being imprisoned in a 10x10 cell for the rest of your life, and how that would affect your own internal sense of "free will", I think you'll realize it's not arbitrary.

One of the debates around free will centers on an idea that free will means actions must be physically random. So, I think people understand that probability and randomness are really important pieces to understanding free will.

The missing link is understanding that probability is a state of mind. It doesn't matter that the physics is deterministic. (Deterministic physics is indeed also responsible for my current unique perception of my consciousness, so deterministic physics can do a whole heckuva lot.)

So, yes, my moment-by-moment decisions in the sea of the universe's physics and other conscious agents are determined by physics, but to all possible computational agents my moment-by-moment decisions and their affect on reality are weighted random.

Free will and freedom are two separate things. The ability to make choices and decisions is separate from your ability to execute them.

That’s why it’s called free “will”. Will is an internal concept, it’s your desire determination, etc for something to happen.

Randomness is not really central to this discussion. What matters is the source, not whether the source is random or deterministic.