Not sure anything has a soul. What's the most compelling scientific theory?
It's not really scientific, but, a soul can be described through a thought experiment.
Focusing only on animate living creatures, there are certain attributes about us that are eternal. For example, I am Daniel son of father's-name and mother's-name. That's true, and always will be true. Nothing can change it even after I pass on, even after my parents pass on. I have certain natural affintites and aversions, certain natural talents, and natural flaws. I will always have these same qualities. After I die, I won't be able to express them, but when I am remembered, if I am remembered accurately, these qualities are part of my identity forever.
The same things can be applied to inanimate objects. If you have children, they probably have or had a favorite cuddly, or favored cuddlies. These cuddlies get named, and the circumstances of how they were added to the family are part of their identity. My daughter had a favorite cuddly named, ba-ba. We had two of them one of them in case one got lost, or needed to be washed. But of course, my daughter could tell them apart, and they became ba-ba and mrs. ba-ba. These were unique because she had them since birth. Just like me, the name, and the origin are part of ba-ba's soul.
Ba-ba has affinities and aversions, talents and flaws as well. Ba-ba handles spills and messes and getting dirty without any complaints or problems at all. However, ba-ba does not do well in the dryer... shrinkage, and the fuzz can melt. These attributes are part of ba-ba, they never change, are always part of the story, always connected to my daughter. And in that way, ba-ba has a soul, given to it from my daughter, when she named it, and loved it for all of these years.
So, there is no real scientific evidence for a soul. But, there is a way to understand it, and observe it as a thought experiment. Are there attributes which define objects, people, animals, plants which are eternal, and always define them? Yes! It begins with a name, and an origin. And what follows from that are distinguishing characteristics which are obvious to those who are in close contact with each of these things.