en.wikipedia.org/wiki/Spit_cake

The claim says Baumkuchen is baked "with baking powder," but the sources I checked describe Baumkuchen differently.

• The Law Library of Congress article on Baumkuchen states: "The ingredients of a Baumkuchen mixture are butter, eggs, sugar, vanilla, salt, and flour. Baking powder finds no place in its creation." It further says this description follows the German guidelines for fine bakery products.
• The German Food Book Commission’s Leitsätze für Feine Backwaren is the relevant German reference for standard composition of fine baked goods. Search results for that document identify Baumkuchen as a Rührmasse (a layered cake batter / sand mixture), not a baking-powder cake.

So while the article is right that Baumkuchen is not a yeast cake, it is wrong to replace yeast with baking powder. The traditional/standard product uses neither yeast nor baking powder as defining ingredients.

The article calls Baumstriezel a "batter made with yeast," but the sources I checked describe it as Hefeteig (yeast dough), not batter.

• Dr. Oetker’s Baumstriezel recipe explicitly describes it as a "traditionelles, süßes Gebäck" in which "ein Hefeteig auf einem Holzspieß gewickelt und gebacken" is used. Its ingredient list is also presented under the heading "Hefeteig für Baumstriezel."
• A German-language Hungarikum publication on Baumstriezel / Kürtőskalács likewise describes the pastry as dough made from flour, sugar, fat or butter, eggs, yeast and milk; after kneading, it is stretched into long strips and wound onto a wooden roller.

That means the article is incorrectly calling Baumstriezel a batter. The product described by these sources is a yeast dough pastry wrapped around a spit/roller.