I'd first argue whether the soul exists at all apart from being a concept.
Well, I was only following your logic
But if there is no soul, why isn't perception a part of the physical world?
This was how science treated energy before Einstein's eq: E=mc^2. He gave it a mass. Then, QFT suggested that atoms consist of excited states of fields. This is what you see all around you.
Generally, physics teachers exercise a "best practice" of teaching that energy is a measurement or abstract representation of physical behavior. For example, they may insist on using a term such as "flow of energy", or they may emphasize that the concept should be used for practical purposes. E=mc^2 doesn't change the point being made. As a less esoteric example: the calorie is considered a form of energy, but that does not mean that the foods we eat consist of any particular object called "calories." If calories did exist in any particular food item, then calories would be absent in food items with entirely different recipes.
To the bold, I would argue that the "soul" includes perception, so according to the logic, perception isn't real either. However, to be fair, it's worth thinking about the distinction between psychological perception and the physiological processes of perception and how one regards the "self". Daniel Dennett wrote an interesting short story to explore the differences, distinctions, and similarities: https://www.lehigh.edu/~mhb0/Dennett-WhereAmI.pdf