So... is RideBack finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: March 30, 2009
Manga finished: October 25, 2008
... 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
In a future dominated by the GGP, Rin Ogata, a former ballerina sidelined by injury, discovers a fascinating machine called a Rideback.
Her innate talent for balance, honed through years of dance, makes her exceptionally skilled at piloting the Rideback.
This newfound ability draws her into a complex web of political intrigue and conflict, putting her at odds with the governing powers.