For me, part of the lessons of the Great War should be the organization of the economy and preparedness for war. To that end I would expect more Germanization and centralization of industry, a German oil company being a high priority. Unlike a communist country the Germans work through private enterprise, elements of state ownership, cartel, bank control, still private yet beholden to the state. At home ensuring refining capacity, oil stocks and refined stockpiles, overseas securing concessions, but also dealing influence. I leverage the relationship with Standard Oil that occurred before and during the Second World War to map out a German-American relationship, adding likely good relations with the Dutch as well.
So I have Esso and Shell sharing the domestic retail market, owning refineries, investing in Germany. A domestic brand or two, the "state" oil company more involved in tank farms, pipelines, refining. I give it a 50% market share at minimum, giving Esso and Shell the rest. And I see Germany investing in America, mostly looking for production but likely a shareholder in Standard. IG Farben was a big shareholder so likely develops Standard's chemical business in partnership, a lot of cross pollination. In Ottoman concessions it is Germany who opens the door for the Americans, leveraging Dollars and expertise to expand German share inside the Arabian fields, looking beyond there for more places to keep Germany fueled. Having so little domestic oil might spur a German specialty in alternative fuels, fuel efficiency, nuclear power, and so on, oil always the Achilles heel.
This should expand into other strategic industries such as tires, chemicals, aluminum, and so forth. Relative to the USA Germany can have one or two big companies in any segment, but I am guessing many partnerships or at least presence in the USA. For me the British Empire is slightly hostile and more closed, the USA is friendlier since Germany bought in the USA during the war, building relationships and dependencies, American industry has a stake in German business so the incest is there. One might do this with a surviving Russia that is not a mortal enemy in addition to or in place of the USA. And I can see a potential relationship with China unless one has Japan side with Germany just to get on a different path. I have a switch as the KMT gets fully in control and outgrows the Germans, the Japanese seek the relationship as their connections with the British weaken. Shifting alliances and relations.