Does Zotero offer installable packages of Zotero Standalone for specific Linux distributions?

No. Zotero distributes Zotero Standalone the same way that Mozilla distributes Firefox: as a tarball that can be extracted and run manually or packaged by others according to distribution-specific standards. Some that have been packaged are

  1. debian
  2. ubuntu

If your distro is not listed above, check if a package is already available. If so, please list it here; if not, please check if a packaging request has already been made (and consider making one if not), follow your distribution's guidelines for requesting a package.