Is there a way to make my media files unsearchable?

If you just want to hide it from standard search engines (stop indexing) then one way I know is to use YOAST SEO plugin. Once you install and activate the plugin, go to the Edit Media page which you do not want to appear in search engine results, and update Meta Robots Index to noindex and Meta Robots Follow to nofollow. Please check screenshot below:

enter image description here

Unfortunately, I do not know (rather there is no way) to bulk edit multiple media files for this.

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