For any plan, Cloudinary supports adding a custom header of X-Robots-Tag (https://developers.google.com/webmasters/control-crawl-index/docs/robots_meta_tag).
You can add
headers=>"X-Robots-Tag: noindex" to all of your uploads for this to be applied.
For our Advanced plan and above, we can add this setting globally. Please reach out to our support team for further details here.
In addition, you can add
noimageindex to your pages (https://support.google.com/webmasters/answer/79892?hl=en).