While working on my website, I noticed that the Database is open access, as all pages can be found in search engines. Is there a possibility to add TXT tags (or specific tags, like Robots Meta Tags (robots.txt)) on search results pages in Omeka S?
You could add a robots.txt file to the root of your Omeka S installation. There is also a module that allows you to manage it from the Omeka admin: Omeka S - Robots