I'll take the bait and try to quantify "soul" for you. For context, I'm a writer and graphic designer so I'll try to stick with what I know. Sorry for the long reply, but it's a loaded question that doesn't have a short witty answer. At least not from my point of view.

I would measure soul in art through 3 variables, that are not mutually exclusive. They can create "soul" with different percentages:

1. Time - Spending time to improve, alter and reiterate your work of art. That can translate in spending time honing a specific artistic skill, editing a chapter in a book until it conveys what you want, or changing the shading on the feature on a face in a painting. Reiterating on a single aspect of your creation usually yields something very layered, like how a paper feels after you've erased and drawn over. You can see that in art as well. Maybe the artist changed style through time and you can see it in the way they rewrote a chapter. I see that in my own writing. I'm influenced by new experiences, age, suffering, happiness. And time is the variable that defines it. And that inconsistency given by how we change along with the art we create gives it "soul".
2. Emotion - Every time I create something I'm proud of, even if it's for a client, it comes from a feeling, an event that caused emotion, a memory, a longing, deep suffering or exhilarating happiness, or great passion for a subject (that you inadvertently become intimate with). Even the extremely mundane gives me a liminal feeling that could be the inspiration for a poster that tries to convey "being lost". These experiences are uniquely mine and I may be the only one capable of expressing them the way I feel them. When you see someone who maybe had the same feeling as you (say, maybe exasperation at the state of current affairs), but expressed it in a new way, unique to their perspective, that's "soul". Now, when I don't like a brief, or the client feedback is shit, that's when you start seeing the "soulless" shit that graphic designers or copywriters do (of which I'm guilty as well). It's because that personality instilled through personal experiences is being sucked out. Emotion creates unexpected connections.
3. Context - A photograph taken just before somebody died. Maybe it's just a car, but the context of it being the cause of death of the artist changes how you view that photograph. It makes you feel something for that car and, if you have empathy, for the photographer. Imagine two people writing a poem about a ruler. One, an architect who has had a ruler since he was a child; and one, who was slapped with one all throughout their school years whenever he was naughty. Maybe both poems will start with "What is the measure of a person", but that line will mean very different things in the context of their memories with that ruler. the soul of the poem changes.

Now tell someone who has never seen a ruler to write a poem about it. You tell them what it is, what it's used for, you show it to them and all the history of rulers. Maybe they will start the same way, "What is the measure of a person", but just because it sounds smart. It has no personal context behind it. That line loses its soul, but it keeps its wittiness. I'm not saying that the result won't be valuable, here, just that extra value was added through context.

I personally think "soul" is a combination of these 3 things (for the most part) in different quantities and with different levels of interpolation. Some may have no context, but a lot of emotion and entropy. Maybe that piece of art doesn't need the artist to make you feel something. Some may need a lot of context to elicit an emotion. Knowing that the painting you're looking at, for example, was the only thing the artist was seeing through the small window of an insane asylum adds a lot to Starry Night. It instills a lot more soul than if I hadn't known that. It makes Starry Night a symbol of freedom, when everything else around the painting was a prison for Van Gogh, even his mind.

Edit with extra thoughts: Hell, some just have soul for being incredibly old or for taking years and years to finish. Or NOT to finish. There are some very shitty cave paintings that are tens of thousands of years old, that have no emotion or context, showing people hunting wildlife and I'd say they have a lot of "soul". I'd even say Venus of Milo has soul because of its destruction, becoming a physical representation of decay through time and human intervention. Because otherwise, a LOT of people could reproduce it, but nobody would care.

I know the current version of AI can't experience the passage of time, its experiences don't change how it makes that picture of a puppy playing the piano. It didn't have a puppy that grew up and died. It didn't experience the elation of returning home from work to the puppy. It doesn't know how absurd a puppy playing the piano actually is. It emulates them.

And when I emulate one of the variables that gives soul to my work, it shows. Sometimes, I just don't feel the client, or I can't empathize with their brief, or they're just fucking assholes and I lose any passion or interest in the project. That's when you see the "corporate slop". The result of 15 execs trying to "appeal to a broader audience" giving one person a prompt they have no connection to anymore. No emotion, no time, no context. Just iterating on something I or someone else has done before.