How can I prevent customers to upload their own images?

The simplest way to do that is to remove the button to upload an image. To do so create some CSS file with the following content:

custom.css

[data-component="image"] [data-component="modal.list-item"]:not([data-image-id]) { display: none; }

Now upload that CSS file to your shop server in a directory which is publicly available. For Shopware this is usually the directory shopware-installation-path/public/ so the file path would be:

shopware-installation-path/public/custom.css

Now get the URL to the CSS file, for instance https://your-shop.de/custom.css and add this CSS file to your product designer configuration (Advanced Tab).

Read more about what you can do with this kind of customizations here: Monkey Patching