The idea of a alternate cold war between The US and a victorious Greater Germanic Reich that stretches from Holland to the Urals has always intrigued me partly due to my family history- so I'll throw in my thoughts here:
Hitler named Goering as his successor on numerous occasions- I imagine that Goering would be sort of a Brezhnev figure that would try and keep the status quo and bleed the eastern reichkommisarants dry before ultimately succumbing to death as a result of his obesity and morpheme addiction sometime in the late 1950;s. I think it would have been inevitable that if this were to happen, Reinhard Heydrich would take over and use the bloated-by-hitler power of the SS to be sort of the "Stalin" figure of the New Order (as in, purging the "old bolshevik" faction of the party, rampantly increasing the holocaust and Generalplan Ost, rapidly increasing Nazi intervention efforts overseas in proxy conflicts with the United States). I could even see Heydrich utilizing the Christian-Pagan divide you still see in Neo-Fascist movements nowadays to launch a "cultural revolution" to finally end the "Kulturkampf" hitler started and make the SS form of Germanic Neopaganism the state religion. Some would say this is far-fetched but I would argue it's no more suicidal of a policy than the Soviet's attempt to turn all of highly, highly religious Orthodox Christian Europe into Atheists.
In regards to "proxy wars", I want to quote Hitler himself here:
"The white races did, of course, give some things to the natives, and they were the worst gifts that they could possibly have made, those plagues of our own modern world-materialism, fanaticism, alcoholism and syphilis. For the rest, since these peoples possessed qualities of their own which were superior to anything we could offer them, they have remained essentially unchanged. Where imposition by force was attempted, the results were even more disastrous, and common sense, realizing the futility of such measures, should preclude any recourse to their introduction. One solitary success must be conceded to the colonizers: everywhere they have succeeded in arousing hatred, a hatred that urges these peoples, awakened from their slumbers by us, to rise and drive us out. Indeed, it looks almost as though they had awakened solely and simply for that purpose! Can anyone assert that colonization has increased the number of Christians in the world? Where are those conversions en masse which mark the success of Islam? Here and there one finds isolated islets of Christians, Christians in name, that is, rather than by conviction; and that is the sum total of the successes of this magnificent Christian religion, the guardian of supreme Truth! Taking everything into consideration, Europe's policy of colonization has ended in a complete failure."
"Never, at any price, should we have put our money on France and against the peoples subjected to her yoke. On the contrary, we should have helped them to achieve their liberty and, if necessary, should have goaded them into doing so. There was nothing to stop us in 1940 from making a gesture of this sort in the Near East and in North Africa. In actual fact our diplomats instead set about the task of consolidating French power, not only in Syria, but in Tunis, in Algeria and Morocco as well. Our 'gentlemen' obviously preferred to maintain cordial relations with distinguished Frenchmen, rather than with a lot of hirsute revolutionaries, with a chorus of musical comedy officers, whose one idea was to cheat us, rather than with the Arabs, who would have been loyal partners for us."
""Our Italian ally has been a source of embarrassment to us everywhere. It was this alliance, for instance, which prevented us from pursuing a revolutionary policy in North Africa. In the nature of things, this territory was becoming an Italian preserve and it was as such that the Duce laid claim to it. Had we been on our own, we could have emancipated the Moslem countries dominated by France; and that would have had enormous repercussions in the Near East, dominated by Britain, and in Egypt. But with our fortunes linked to those of the Italians, the pursuit of such a policy was not possible. All Islam vibrated at the news of our victories. The Egyptians, the Irakis and the whole of the Near East were all ready to rise in revolt. Just think what we could have done to help them, even to incite them, as would have been both our duty and in our own interest! But the presence of the Italians at our side paralysed us; it created a feeling of malaise among our Islamic friends, who inevitably saw in us accomplices, willing or unwilling, of their oppressors. For the Italians in these parts of the world are more bitterly hated, of course, than either the British or the French. The memories of the barbarous, reprisals taken against the Senussi are still vivid. Then again the ridiculous pretensions of the Duce to be regarded as The Sword of Islam evokes the same sneering chuckle now as it did before the war. This title, which is fitting for Mahomed and a great conqueror like Omar, Mussolini caused to be conferred on himself by a few wretched brutes whom he had either bribed or terrorized into doing so. We had a great chance of pursuing a splendid policy with regard to Islam. But we missed the bus, as we missed it on several other occasions, thanks to our loyalty to the Italian alliance! In this theatre of operations, then, the Italians prevented us from playing our best card, the emancipation of the French subjects and the raising of the standard of revolt in the countries oppressed by the British. Such a policy would have aroused the enthusiasm of the whole of Islam. It is a characteristic of the Moslem world, from the shores of the Atlantic to those of the Pacific, that what affects one, for good or for evil, affects all.""
TL;DR While Hitler called efforts to ally with anti-colonial forces in Mein Kampf to be equivalent to working with a "coalition of cripples", once he was actively fighting the war National Socialism started adopting alot of anti-colonial talking points. I can very easily imagine a victorious Nazi state supporting Fascist anti-colonial movements all throughout the third world, ex. the Ba'athists or Golden Square in Iraq, the Boers in South Africa, the more radical Hindu fundamentalist movements in India. As a matter of fact, contrary to the TNO scenario of a vietnam-esque quagmire in South Africa, I would imagine the big "proxy conflict" for this cold war would be in India between not only Democrat and Fascist indian forces- but also different Muslim, Hindu, and Sikh militias. Britain even without Sealion (which never would have happened anyways) would regardless be running around losing colonies like a chicken with it's head cut off anyways- fuck, they were like that IRL.
Also the AK47 would probably never be invented- the "ultimate bad-guy gun", to quote the late R. Lee Ermey, would be the FN FAL or some derivative of the STG44.
I could go on for hours about different things regarding pop culture, geopolitics, the economy, etc. in such a alternate history scenario but I've sperged enough here so I'll wait for feedback before giving more thoughts.