So... is Horimiya finished or not?
YES, it is finished.
Why?
The anime finished after the manga:
Anime finished: April 04, 2021
Manga finished: March 18, 2021
MangaUpdates contains information about the anime adaptation and indicates that it is complete.
Watching Order (by release date)
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Synopsis
Horimiya explores the unexpected connection between two high school students, Kyouko Hori and Izumi Miyamura, who present very different personas to the outside world.
Hori is popular and admired, but burdened with household responsibilities, while Miyamura is quiet and unassuming, hiding a more rebellious side.
When they discover each other's hidden selves, they forge an unlikely friendship based on mutual understanding and acceptance.
The story follows their developing relationship as they navigate school, social pressures, and reveal more of their true selves to each other, finding comfort and support in their unique bond.