But though that is the colloquial meaning, it doesn't line up with what people say they want: you want to make your choice according to your own reasons. You want free choice. But unless your own reasoning includes a literal throw of the dice, your justifications deterministically decide the outcome.
"Free will" is the ability to make your own choices, and for most people most of the time, those choices are deterministic given the options and knowledge available. Free will and determinism are not only compatible, but necessarily so. If your choices weren't deterministic, it wouldn't be free will.
But when you probe people, while a lot of people will argue in ways that a philosopher might call compatibilist, my experience is that people will also strongly resist the notion that the only options are randomness and determinism. A lot of people have what boils down to a religious belief in a third category that is not merely a combination of those two, but infuses some mysterious third options where they "choose" that they can't explain.
Most of the time, people who believe there is no free will (and can't be), like me, take positions similar to what you described, that - again - a proponent of free will might describe as compatibilist, but sometimes we oppose the term for the reason above: A lot of people genuinely believe in a "third option" for choices are made.
And so there are really two separate debates on free will: Does the "third option" exist or not, and does "compatibilist free will" exist or not. I don't think I've ever met anyone who seriously disagrees that "free will" the way compatibilists define it exists, so when compatibilists get into arguments over this, it's almost always a misunderstanding...
But I have met plenty of people who disagree with the notion that things are deterministic "from the outside".
Approaching this subject from a rational perspective divorces you from subject and makes it impossible to perceive. You have to immerse yourself in it and one way to do that is magical practice. Having direct experience of the universe responding to your actions and mindset eventually makes it absurdly clear that the universe bears intelligence and it's in this intelligence that free will operates.
I'd never thought before now to connect magic this directly to free will. Thanks for the opportunity to think this through! If you're interested in a deeper discussion, happy to jump on a call.
From the outside, this is indistinguishable from randomness. But from the inside, the difference is that the individual had a say in what the action would be.
Where this tends to get tangled up with notions of a soul, I think, is that one could argue that such a free choice needs some kind of internal state. If not, then the grounds by which the person makes the choice is a combination of something that is fixed and their environment, which then intuitively seems to reduce the free-will process to a combination of determined and random. So the natural thing to do is then to assign the required "being-ness" (or internal state if you will) to a soul.
But there may exist subtle philosophical arguments that sidestep this dilemma. I am not a philosopher: this is just my impression of what commonsense notions of free will mean.
Same as that is not the lived experience. I notice that I care about free choice.
The idea that there's no free will may be a pessimistic outlook to some but to me it's a strictly neutral one. It used to be a bit negative, until I looked more closely that there's a difference between looking at a situation objectively and having a lived experience. When it comes to my inclinations and how I want to live life, lived experience takes precedence.
I don't have my thoughts sharp on it, but I don't think the concept even exists philosophically, but I think that's also what you're getting at. It's a conceptual remnant from the past.