So... is Groove Adventure Rave finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: September 28, 2002
Manga finished: July 27, 2005
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
Long ago, devastating artifacts called Dark Brings caused immense destruction. Now, a villainous group called Demon Card is after these dangerous stones.
A young man named Haru Glory is chosen as the Rave Master, destined to wield the power of the Rave Stones, which are the only things that can destroy the Dark Brings. Unfortunately, the Rave Stones were scattered years ago.
Haru, along with his unusual dog Plue, a spirited young woman named Ellie, and a notorious thief named Musica, embark on a grand adventure. Their goal is to find the scattered Rave Stones and stop Demon Card from using the Dark Brings to cause chaos and suffering in the world.