Is There a Baroque Manga or Anime?
The manga is Baroque: Ketsuraku no Paradaimu (The Missing Paradigm), written and drawn by Shinshuu Ueda and serialized in Square Enix's Monthly GFantasy. Square Enix published it in three volumes from March 2001 to March 2002, and it was reprinted in two volumes by Reissue Dot-Com in January and March 2017, a reprint that exists because the originals had become genuinely scarce. Fan accounts of buying it tell the story plainly: the volumes cost about as much as the game.
Ueda's manga retells the descent with room the games never had, expanding the cast's backstories, and it preserves the tone: sympathetic to the deformed and the dispossessed, uninterested in explaining itself. Early volumes were scanlated by fans; the later ones largely were not, owing to how rare the books had become, so the English doorway into Baroque's manga remains half open.
The anime does not exist. No television series, no OVA, no film was ever produced, in the Saturn era when such adaptations were routine or since. Baroque's moving images remain the games' own: the 1998 CGI films by Inertia Pictures and Kito's team, the remake's Point Pictures opening, and that is all. The other prose branch, Mariko Shimizu's prequel novellas, is covered on the spin-off shelf.