So... is Arabian Nights: Sindbad no Bouken (TV) finished or not?
NO, it is not finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Arabian Nights: Sindbad no Bouken tells the story of Sindbad, a young and curious boy living in Baghdad.
Inspired by his uncle's adventures and a yearning to see the world, Sindbad decides to become a sailor.
He leaves home, joins his uncle Captain Ali's crew, and embarks on a journey across the seas with his myna bird, Sheila, in search of exciting adventures.