So part 2 of my ramblings:
Regarding the great powers Germany will be mostly focused on Europe, so the relationship with the USA should remain vaguely friendly with a dose of economic rivalry, but of minor importance. Japan will depend, but lets keep Asia for later. Overall Germany despite Versailles is leaning more Anglophile than not and as Germany will not be a naval threat any time soon there should be little conflict. With the USSR there was a good cooperation out of need throughout the twenties, but the different ideologies made it uncomfortable from the start and as that need became less pressing even before 33 cracks in the cooperation became more visible. A total break might or might not happen, but a cooling of relations is certainly to be expected in the medium term. With Italy the one big zone of conflict is Austria, beyond that it is no immediate problem. Relationship is unlikely to be friendly, but I would anticipate mostly attempts to peacefully contain Italy.
France is the most interesting. Of course there are the lingering animosities, most recently over Versailles. But there also were cautious steps towards a friendlier, closer relationship on both sides. With Versailles out of the way and Germany apparently gaining the upper hand in Europe, towards the end of the 30s more French politicians might warm to the idea of close cooperation as a possibility to restrain Germany peacefully. And on the German side it would be logically to embrace that to avoid a new encirclement. A looser version of the modern Franco-German axis for European integration might result. Of course that requires the right politicians to be in power in both countries at the right time. Alternatively France might try to retain a degree of encirclement. At least for the 30s a degree of that is likely even if relationship thaws (see below on the Balkans). Worst case France finds common cause with the USSR in Europe and we are almost back in 1914, but I would not see it as most likely result.
An issue with any great power might occasionally be the widespread presence of German military advisors everywhere from Afghanistan to South America, which might remain more present without the breakneck rearmament of otl. If that intersects with a great power´s interests, it could lead to tensions, but should mostly not be a dealbreaker.
Beyond that in Europe a resurgent Germany likely will in the late thirties start to compete with (especially) France and Italy for influence in the Balkans. The starting position for that is pretty reasonable, though I would not dare any firm predictions on where Germany succeeds. Most likely to fall into the German camp are imo Yugoslavia, as Germany will probably be seen as best shield against Italian aggression. My gut says that Hungary is the least likely to align with a democratic Germany, as after achieving its own revisionism Germany does not need a destabilising revisionist in its backyard. Of course at peace Germany has no pressing needs like access to oil in that region, so it can play realpolitik and give support however it offers the most benefits. It just needs to keep France forming an Anti-German bloc and has no interest in facist Italian control of much of the region.
Germany will most likely keep out of a Spanish civil war although the way that goes will already be influenced by the fact that Germany is unlikely to offer active support. OTL Germany was a core component in airlifting Franco´s troops from Morroco to Spain and provided material support even when military and foreign office were still opposed to active support. And of course later on the presence of German troops helped the nationalists. After a Spanish civil war German governments might actually be more comfortable in dealing with a nationalist government, especially if butterflies mean the facists are not the dominant faction of the nationalists, if the alternative is the radicalized Leftists that came to dominate the Republicans during the war. Not enough for active support though nor will the hope to moderate the Republicans suffice to make an intervention on that side.
Northern Europe is a safe region for German interests: Norway orientates itself more towards Britain, but that is only an issue if Germany and Britain are at odds. Things with Denmark have been patched up. Sweden and Finland are generally friendly, though with the latter the everpresent danger is to be drawn into a conflict with the USSR, thus Germany might keep a friendly distance unless active containment of communism becomes a major political concern in Germany. The same is generally true for the Baltics, a decent relationship, minimally impacted by the unimportant Memelland, but no interest at the beginning of the 30s to make front against the USSR. That can change of course and the Baltic states easily can fall into the German orbit.
Outside Europe German interests will be mainly commercial. Out of necessity Germany in the twenties German business were among the ones with the most global outlook, e.g. the Luft Hansa was the first airline to attempt a truly global presence, even if mostly through local subsidiaries. The presence of military advisors almost everywhere also helped in spreading German influence as they often had technical and economic advice in their backpockets and the industry contacts they provided were German firms or their fronts in other European countries. The depression put a dampener on global business aspirations, but only the nazi economic and monetary policies and of course the war really cut into that. Without that the globalisation of German business likely will accelerate as the economy recovers and German global diplomacy will be mainly in support of that.
The one really big problem Germany has globally is China. There was a lobby in Germany even in the early 30s that argued keeping China down was necessary or it would become too powerful fast and thus favoured aligning with Japan in Asia to achieve that. That some of those also wanted Japanese expertise to rebuild the German navy might have influenced them. But on the business side the Chinese market was seen as the more promising one and the army and arms industry, influenced by the military mission to China, likewise leaned towards Nationalist China. In general it seems most likely that a Democratic Germany would align somewhere between support for the nationalists and for the US open door policy, favouring the former as long as it does not hinder business. In case of Japanese aggression that support will IMO continue, though the extent might vary: The mission will certainly be allowed to remain. US diplomatic initiatives against Japan should be supported, maybe even some own proposals made. War material will be supplied, though with how much generosity? Volunteers may potentially be allowed, less so that Germany actively forms volunteer units. Active participation in the conflict is almost out of question, except perhaps in concert with other (European) great powers under unusual conditions.
Of course if Germany is not forced to choose it will try decent relationships with both countries as business and relationships with both countries were good until being friendly with one was an unfriendly act towards the other.
Last and least there are colonial ambitions as I forgot it in the revisionism post. There was a colonial lobby in Germany and the German government tactic in the 20s was to try getting into the league mandate administration and through that get control of some formerly German mandates, mainly Cameroon. Flanked was it with a government supported buyback scheme for private plantations to create preserve a pro-German lobby at least in Cameroon. That scheme fell victim to the depression. Inadvertantly a bit of "pro"-German nostalgia (not as bad as our new rulers) was helped along that way. But overall the topic was never really important on the government level and imo that will always be the case. Successfully getting the mandate over a former colony might be a nice success if it happens, but it will only as a side effect of some other diplomatic shenanigans.
