So... is Haikara-san ga Tooru finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: March 31, 1979
Manga finished: January 01, 1977
... But MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Haikara-san ga Tooru is a story set in 1920s Japan, following the life of Benio, a strong-willed and independent young woman determined to forge her own path.
Initially clashing with Shinobu, a charming half-German soldier, Benio's life takes an unexpected turn when she discovers they are betrothed in an arranged marriage.
The narrative then explores Benio's journey as she grapples with the complexities of marriage, family expectations, and her own aspirations during a time of social change and unrest.
Amidst the challenges of war and adapting to her new circumstances, Benio must navigate her relationship with Shinobu and find her place in a society on the cusp of transformation, all while a major historical event approaches.