So... is Oniisama e... finished or not?
YES, it is finished.
Why?
The anime finished after the manga:
Anime finished: May 31, 1992
Manga finished: August 01, 1974
MangaUpdates contains information about the anime adaptation and indicates that it is complete.
Watching Order (by release date)
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Synopsis
Oniisama e... follows Nanako as she begins her life at the exclusive Seiran Academy. Expecting a positive experience, she instead finds herself caught in complicated social dynamics and unexpected challenges.
Chosen for a coveted spot in the school's Sorority, Nanako quickly becomes the target of jealousy and resentment, particularly from a classmate named Aya.
To navigate the difficulties of her new environment, Nanako finds solace in writing letters to her former teacher, whom she considers a brother figure. She also relies on the support of a small circle of close friends.
The story explores themes of bullying, social pressure, and the trials faced by a young girl as she attempts to adjust to a demanding and unforgiving school setting.