So... is Hanayamata finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: September 23, 2014
Manga finished: February 24, 2018
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
Hanayamata follows Naru, a shy 14-year-old girl who feels ordinary and longs for a magical transformation to become more confident.
Her life takes an unexpected turn when she meets Hana, an energetic transfer student from America with a deep passion for yosakoi, a vibrant Japanese dance.
Hana wants to start a yosakoi club at their school, and despite her initial reservations, Naru is drawn into Hana's enthusiasm and the beauty of the dance.
The anime centers around Naru's journey of self-discovery as she embraces yosakoi, helps Hana realize her dream, and finds the courage to step outside her comfort zone.