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. See our Upload API docs for more information on this and please use our Explicit API for existing assets.
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).