So... is World Dai Star 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
World Dai Star tells the story of Kokona Ootori, a young girl with aspirations of becoming a World Dai Star – the most celebrated performer in a world captivated by musical theater.
Facing numerous setbacks, Kokona finally gets another opportunity to audition for a prestigious theater troupe.
Driven by her friendship with Shizuka, she embarks on a journey to hone her acting skills and pursue her dream.
However, Kokona will face fierce competition from other talented aspiring performers, including the German prodigy Kathrina Griebel, as she battles for a coveted spot on stage and strives to prove herself in the demanding world of theater.
Her journey focuses on her struggle to rise above the competition and earn the recognition she craves.