Zotero doesn't index much, it primarily looks up identifiers - usually doi's, but also ISBN's, and then fetches metadata, pretty much like Calibre does. For journal articles and books it does an excellent job, but for content without such an identifier, such as a web page, it'll attempt to parse metadata but often gets it wrong or in the wrong fields - it's often faster to just fill in the fields manually.
I'm not sure what that has to do with Calibre either, but Zotero will happily store content internally (inside a Mozilla profile, a bit black boxed, although you can get it out), externally (in a directory structure of your choice), or as references to existing locations - such as in Calibre, as url's. It does cope admirably with a much wider range of documents and document types than Endnote though.
The biggest problem I can see is that the majority of metadata sources available to Calibre, even via plugins, do not support the information required for the majority of formal citation standards, at least not without a ton of custom columns and manual entry. Off the top of my head things like publisher location, edition, chapter authors, journal issues don't fit neatly into Calibre's columns - and why would they, they're not that interesting outside of when you have to cite them.
So if you're going to do a ton of manual entry anyway, you may as well be doing it in a tool specifically for the intended purpose. (And if you don't like Zotero, try Mendeley or Citavi, all of which are better for multiple formats than Endnote imo.)
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