Füst is Jenka's pet bear. Unlike Jenka herself, Füst doesn't appear to be a Construct, but rather a hunk of relatively natural bear meat, although it's hard to be sure. He also doesn't share some of the other Jägermonster characteristics, like speaking with a German accent -- his "RHAAA!", "WHUMF!", etc., appear to be standard humongous bear noises. On the other hand, he's about twice the size of any real-world bear, so some degree of Sparky enhancement isn't out of the question. He's categorized among the Wild Jägers either way.
Jenka is riding aboard Füst when they crash ✣ the party at Zumzum, important for plot development because it allows the Jägers to meet Agatha Heterodyne and start getting the idea that maybe she really is the Heterodyne heir that they've been seeking. (Füst doesn't exactly endear himself to the townsfolk on this occasion, but oh well.) He also appears (offstage) later when the Jägers are the first to notice ✣ that Mechanicsburg is under attack by the War Stompers under Rudolf Selnikov. We'll probably see him again.