I can speak to Germany as someone from Germany who went through the German school system and history lessons about Germany in that context. I'll cite sources too, of course.

German bureaucracy definitely predates WW2. If we check the abstract of this article https://link.springer.com/chapter/10.1007/978-1-349-01476-7_4 it tells us that Prussian bureaucracy was established in the first quarter of the eighteenth century.

Note that "Germany" as a unified country didn't exist until later. Like, say, 1871 when Bismarck united all the individual German states against the "arch nemesis" France. But when that happened, it happened under Prussian leadership, and its system of governance was extended across the Reich.

Bismarck then worked hard to create a strong bond between the citizens and the state; the authoritarianism and the almost blind obedience shown towards the state and the rules has been the subject of many German works of art, such as the movie "Der Untertan" (The subject) and the play, based on a true story, "Der Hauptmann von Köpenik". Anyway, this ensured that the institutions based on bureaucracy would remain strong and survive all the following turmoil of the WW I, the revolution of 1918, the Weimar Republik, the Great Depression.

Nazi Germany, too, was a very bureaucratic place. Maybe most starkingly demonstrated in the meticulous paperwork for all the carnage committed in the death camps. They worked hard to make the usually neutral civil servants into "soldiers" of the state as well (see eg https://www.jstor.org/stable/1881401?seq=1)

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There is a nice essay on this. The original website is down, but here is a cached version: http://webcache.googleusercontent.com/search?q=cache:fNSwloh0KfYJ:www.galorebot.com/bureaucracy/essay.htm+&cd=2&hl=en&ct=clnk&gl=ca&client=safari

Lots of further sources in that one, too.

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So in conclusion, Germany was definitely bureaucratic before WW2. And still kinda is. Our legalese has some absurdly weird expressions. Like "If a public servant dies while on a business trip, the business trip is considered ended." https://www.dw.com/en/germans-and-bureaucracy/a-16446787