It seems you're facing a fundamental issue: originally, the layer was placed as a JPG or flat image format, which doesn't support layering, rather than being converted to a Smart Object. Photoshop is prompting you to save the file in a format that supports layering. The concept of a Smart Object is to preserve the original, but this isn't feasible since you've added a layer or data to a file format that can't handle multiple layers.
The solution is to either merge layers or recreate the layer you wish to replace. For instance, you could convert the Smart Object to a normal layer, rasterize it, and then convert it back to a Smart Object. This method will allow you to open the Smart Object, place an image, and save the changes. However, this isn't advisable as your file size will significantly increase with each new image and person added. A better approach would be to flatten the image after placing the replacement photo.
Incidentally, if all the replacement files share the same dimensions and resolution, you could utilize the Replace Contents command to substitute the photo instead of editing the Smart Object repeatedly.
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