Zotero can't generate multiple different bibliographies in the same document. The standard way to handle this is to keep every chapter in a different document, generate the bibliography there, then make copies of each chapter (don't skip that step), unlink citation in all those copies and merge them into a single document.
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The standard way to handle this is to keep every chapter in a different document, generate the bibliography there, then make copies of each chapter (don't skip that step), unlink citation in all those copies and merge them into a single document.