So... is Ginga no Uo Ursa Minor Blue finished or not?
NO, it is not finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Urey, a boy residing in a lakeside laboratory with an elderly mentor, discovers an anomaly affecting the stars of Ursa Minor.
These stars are vanishing, and the constellation is morphing into the shape of a fish.
Driven by a desire to restore the stars, Urey and his companion embark on a journey across the Milky Way.
Their quest is to find the origin of this strange fish and, hopefully, reverse the celestial decline.