You refer to the Easter Message of March 1917? Didn’t he make that promise only based on the advice of Bethmann Hollweg to influence the public opinion? And after BH was sacked, Hindenburg and Ludendorff gained even more power, as we see in the Treaty of Brest-Litovsk which was in fact the execution of the far-right war goals. And the Hindenburg-Ludendorff-regime will only be stronger if Germany wins. Won’t this mean a continuation of an authoritarian state?
As I understand it the H-L "regime" was established on legal grounds at the behest of the civilian government, and would immediately hand back power after the war concluded. Hindenburg would almost certainly not become a dictator, as he was first and foremost loyal to the Kaiser and would go along with his wishes, however reluctantly, should Wilhelm stay true to his promises to introduce reform. Even after the abolishment of the monarchy, Hindenburg wrote to an exiled Wilhelm asking for permission to run for the presidency in the 1920 election. Ultimately I expect gradual liberalization to be accepted -- grudgingly -- by the conservative establishment. If a regression into authoritarianism
does occur, I expect it would be a result of a failure to address whatever Great Depression analogue occurs ITTL, rather than through a continuation of the wartime military dictatorship.
How about the old traditionalist (and authoritarian) Prussian and German militarist culture? Will this dominate Germany and Eastern Europe?
"Dominate" is a strong word, as I do think the "Prussian militarist" character of Germany will soften somewhat over time with rising social democratic influence, but I still expect it to be rather influential. Germany's pride in its armed forces will have been vindicated and strengthened by its victory, and with the need to garrison forces in the East to safeguard their conquests I wouldn't be surprised if we saw a "support the troops" mentality such as we see in the modern US emerge in ATL Germany. And while I do expect German culture to become quite popular across Europe, I can also see growing resentment towards it depending on Germany's treatment of its client states.
Also, I would expect German to take the place of OTL English in becoming the de facto lingua franca of Europe (at least everything east of the French, who I expect would refuse to learn it out of spite). This is a possibility that's always interested me in CP victory timelines -- German takes the place of English as the European lingua franca and German media becomes the cultural standard on the continent, with the Anglosphere being much more culturally isolated as a result.
Off course I think it is also important what happens with Austria, Russia, America etc., but that is a question of debate. I think indeed broadly speaking we can see how the culture and society in Europe and the world will look like.
Absolutely. Of particular importance IMO is what happens in the case of Russia. If the Bolsheviks or any other radical leftist government take over then we can expect Germany and the rest of Europe to go through some sort of Red Scare with all that entails. If there's a strong, atheistic communist power to the East then I'd expect German society to become more militaristic, religious, and socially conservative as a reaction.
As for Austria, by 1918 they were tied to Germany at the hip and were by all accounts a satellite state. For the first couple decades or so I imagine that they'll be dancing to Berlin's tune.
Moving on to the US, I'll assume from your scenario that they remained neutral due to no resumption of USW. Continued neutrality has pretty big implications for the US. For one, there's the obvious matter of German-American culture not being suppressed to near non-existence. Winning cultures are sexy, so I'd expect Americans to take much greater pride in their German character, with events like Oktoberfest gaining as much popularity as, say, St. Patrick's Day. We also probably would not see Prohibition, or at least if we did it would not include beer. This prevents the meteoric rise of organized crime in the US, and "gangsterism" never becomes the cultural phenomenon it did. There's also a greater likelihood (though not a guarantee) of the US adopting universal healthcare, as the idea was gaining traction in the country before it became tainted by its association with the hated Germans. Ditto for public universities. Other differences are that the US has not spent an incredible amount of money and resources, nor lost over 100,000 young men in their prime, in fighting an unpopular war. If the Democrats are still in charge they're likely praised for keeping the country out of Europe's madness, and so the Progressive Era may continue on without being discredited as in OTL. I expect the US to build a huge fleet so that the Germans don't get any funny ideas, but otherwise remains staunchly isolationist. If you can't tell already, I'm of the opinion that WW1 was a very unhealthy experience for the US, and that American society would be in a much better place without the OTL entry into the war.