So... is Ginga Sengoku Gunyuuden Rai finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: March 31, 1995
Manga finished: January 01, 2003
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Ginga Sengoku Gunyuuden Rai transports viewers to a futuristic galaxy deeply inspired by feudal East Asia.
Multiple powerful factions, reminiscent of warring states or clans, are locked in a struggle for dominance across the stars.
At the heart of this conflict is Rai, a samurai whose journey intertwines with the ambitions of these factions as they vie for control of territories and the ultimate prize: the Empire.
The anime explores Rai's life amidst this turbulent backdrop of space-faring societies and ancient traditions colliding in a grand, intergalactic power struggle.