Photography stealing someone’s soul is easy to discount as an obvious misconception, but if you think of “soul” as a shortcut metaphor for some difficult to describe sociopsychological phenomena then there is some food for thought in it.
First, for most of us in daily life, once you know you are being photographed you exit any context you were in and enter the new “I am being photographed” context. In some important way, you are stolen from the world around you for a period of time. Your body is still present, but you might be thinking about how this all would look at any later time. This does not apply when photography is specifically arranged by you (common in analog era), or if you are unaware of being a subject photographed (but there may be other concerns about that[0]).
Second, a photo/likeness of you is a proxy allowing other people to relate to you. Keeping in mind that we only ever relate to images/models that we build of each other in our minds (we have no “direct access” to other people), in this case a photo is a shallow (there is little other information than appearance) but weirdly high fidelity (for sighted people) model of you. This is not an issue if the photo is kept just by people you know (common in analog era) or after you are dead, but otherwise if published[1] it means people can somehow relate to “you” without the actual-you knowing or having met them. Some people may feel some sort of satisfaction from this, others it can make uncomfortable.
Third, as someone noted, soul could map to another nebulous concept: identity. It could range from problematic cases (someone pretending to be you to resell work you made) to twisted but benign (stories about people making fake profiles pretending to be successful SV employees come to mind).
[0] If you are secretly photographed[2], this can happen for a number of reasons. Some may imply a missing interaction (if that photographer could not photograph you, maybe they would talk to you instead). Some may be done with intent of sharing your photo in unknown context where again people may relate to you in specific ways that can be unpleasant (e.g., mockery).
[1] Now when generative models start to be trained on what we thought is our private photos, the idea of “published” is blurred.
[2] In most cases here “photo” can be swapped with “video”.