The server you linked seems to run nginx. While the old server also seems to be nginx, that server is a bit more complicated than your standard apache (moving the files in the webroot might not be enough).
Are you sure you configured the new server correctly?
Here’s a guide: Running Kirby on a Nginx web server | Kirby CMS
I’m thinking about configuration because the error page you’re getting for the images directly comes from nginx, while I’d expect either an image or at worst an error message from Kirby. It looks like requests to the media folder aren’t handled by the kirby “index.php”, while they really should, at least for non existing files.
