So... is Spriggan (ONA) finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: June 18, 2022
Manga finished: January 25, 1996
... But 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
A powerful, ancient artifact has been discovered, and a shadowy organization called ARCAM is trying to protect it.
Unfortunately, a militaristic group from the U.S. wants to seize the artifact for their own nefarious purposes, seeking global dominance.
ARCAM's only defense lies with their elite operatives, the Spriggans. One such Spriggan, a young Japanese agent, joins forces with a French Spriggan to thwart the enemy's plans.
They must confront a genetically modified adversary with incredible psychic abilities before he can exploit the artifact and unleash chaos.