So... is Himegoto finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: September 29, 2014
Manga finished: June 27, 2015
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
Hime Arikawa, burdened with his parents' massive debt and relentlessly pursued by loan sharks, finds himself rescued by the Shimoshina High School student council.
In exchange for paying off his debt, the student council demands Hime transfer to their school and become their "servant."
This "servant" role involves Hime cross-dressing throughout his high school life as part of the student council's activities.
Hime must navigate his new school, endure the antics of his classmates, and fulfill his obligations to the student council while grappling with the challenges of his unusual situation.