So... is Fushigi no Kuni no Miyuki-chan finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: June 21, 1995
Manga finished: June 10, 1995
... 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
Miyuki-chan, a seemingly ordinary girl, experiences an extraordinary event when she's unexpectedly whisked away to a bizarre, alternate dimension.
This isn't your typical isekai; the world she finds herself in is populated entirely by women.
To further complicate matters, these female inhabitants are all infatuated with Miyuki.
Adding another layer of peculiarity, there's yet another strange world existing behind a mirror, hinting at even more surreal adventures for Miyuki to navigate. It seems like being late for school led to a very unusual detour.