So, I would say that broadly, the Wikipedia article this question is drawn from takes the traditional narrative of Prusso-German history at face value, and that makes it hard to understand this seeming dichotomy.

The idea that Prussia was a purely authoritative and conservative state before 1918 relies on a reading of German History that relies heavily on the idea of the Sonderweg. Essentially, the Sonderweg, or special path, theory, argues that Prussia used the power wielded by a militaristic conservative elite to gather the military resources sufficient to create Germany through military success. In essence: Prussian power in Germany followed a special route that allowed the Germans to ignore the democratic and anti-authoritarian traditions that had evolved in western Europe.

This idea as the explanation for the rise of the Nazi movement and the horrors of German actions during the Nazi era dates to the immediate post-WW2 era. More recently, German and English language historians have been challenging the Sonderweg interpretation of the creation of Germany. There was a liberal tradition in Prussia as well, and historians, such as Christopher Clark, have tried to re-write Prussian history as a tension between liberal and conservative forces. Frederick II of Prussia, in addition to being a warlord and conservative monarch, was a relatively tolerant and enlightened monarch by the standards of his age, who attempted to end serfdom in Pomerania, and sided with commoners against the Junker class in legal disputes. Both conservative and liberal strains of thought and power were in tension in Prussia.

So- as opposed to trying to say: "Prussia was conservative before 1918, why did it become a bastion of left/democratic government after 1918?", we should instead look at this tension. In Prussian cities, starting with the election of 1893, the SPD (the Socialist Party) began to win elections. Before that, Prussian liberals had unified in opposition to Bismarck behind the banner of the DFP (German Progressive Party). Berlin, Breslau, Königsberg and Stettin all voted for the SPD in that 1893, and continue to vote for the SPD through the election of 1912. While rural areas still voted for conservative parties, the urban spaces of Prussian were establishing a more progressive tradition. Thus, Prussian election patterns broadly fit models that seem more modern: the urban centers vote liberal, the rural areas vote conservative.

With this in mind, the country-wide success of the SPD in the 1919 elections seem less shocking with reference to Prussia: conditions in the country has a whole had convinced the rural voters to (temporarily) side the city-dwellers. Otto Braun, a socialist, was the prime minister of Prussia from 1920 to 1932. Braun, a career SPDer who had been advocating for workers since the 1880s, built a coalition of socialists, liberals, and centrists to govern Prussia in the Weimar era. After the Nazi rise to power, Braun was ousted by Franz von Papen, and fled to Switzerland. He attempted to convince the allies to restore his democratic government at the end of the war, but they had decided (influenced by the idea of the Sonderweg) that Prussia was essentially conservative, and needed to be destroyed.

I hope this helps- let me know if you have further questions!

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Dietrich Orlow, Weimar Prussia, 1918-1925: The Unlikely Rock of Democracy, Pittsburgh University Press, 1986.

Jonathan Sperber, The Kaiser's Voters: Electors and Elections in Imperial Germany, Cambridge University Press, 1997.