So... is Sasurai no Taiyou finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: September 30, 1971
Manga finished: August 01, 1971
... But MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Two girls are born in the same hospital, one into wealth and the other into poverty. A vengeful nurse swaps the babies at birth, setting their lives on drastically different paths.
Years later, the girls' lives remain connected, with the girl raised in wealth treating the other poorly. Despite their differences, both share a common ambition: to become singers.
The story explores the intertwined destinies of these two young women, the consequences of the nurse's actions, and their shared dream in the face of their complicated relationship.