I have never heard that German offered to partition Greece with Yugoslavia. What is your source? When Yugoslavia signed the Tripartite Pact, it made a lot of effort to include language that it would not allow Axis troops to transit through Yugoslavia and that Yugoslavia would not provide any troops for war.
Hitler wanted to make sure that Germany's southern flank was secure before operations against the Soviet Union began. Even before the Yugoslav Crisis, he made plans to invade Greece through Romania and Bulgaria. This was done as early as December 1940. With no Belgrade coup, Bulgaria and Germany likely invade Greece anyway around the same time as they did IOTL and with the same results.
In any event, a Yugoslavia essentially friendly to Germany but neutral will survive the war intact. Not much changes. Nothing major affects Crete, the eastern Med, or Barbarossa. Without needing to station garrisons in Yugoslavia, the Germans have slightly more manpower to use in USSR. Still won't change anything. Maybe the most diehard fascists in Yugoslavia join up for a Yugoslavian version of the Azul Division and march off to die in the snows of Russia.
Yugoslavia probably enters the war on the Allied side in late Summer 1944 after it is obvious both the Red Army is approaching from the east, and the Allies through Italy. If so, Bulgaria might be more willing to defect as well and also avoid the Red Army from occupying it. In any case, Yugoslavia retains its independence. This slightly changes the balance of power in Europe. Also, Trieste likely becomes part of Yugoslavia.
Yugoslavia will be included in Marshall Plan aid and likely be a member of early pan-European cooperation. This will help it greatly because Yugoslavia lacked a lot of infrastructure and industrialization.
It will probably suffer ongoing ethnic problems, but nothing that can't be handled. It will enjoy an economic boom as most of Europe did from 1948-1970. That will help quell tensions.
Politically, it will probably develop into a mature democracy given time. There will probably be lots of protests before then. I suspect bolstering democratic institutions will happen in order to keep the US happy. The Yugoslav Communists will probably become legal with Tito as its leader. I suspect it will be initially popular like the French and Italian Communist parties, but not be able to actually win elections although the first decade or so of elections might threaten them. Eventually, a democratic Socialist opposition will take the spot like in France. That's the best case scenario. Worse case is like Greece.
There is no Titoist split, so Stalin will find some other excuse to purge people and have show trials in the European Communist parties under his control. I don't expect Stalin's empire to be much different.
Will Yugoslavia join NATO? Probably. That will give some strategic depth. It will also provide NATO with direct access to Hungary and Romania. It might make intervention in a Hungary 1956 scenario more plausible if the US wants to put pressure on the Soviets. I still wouldn't expect anything like war to start over such a scenario, but it might allow the US to bluff Moscow. If so, we start having major butterflies. Most likely Moscow still crushes any revolt. Cold War develops similarly as in OTL.
The main changes will not come with the international situation, but how Yugoslavia develops internally and likely avoids the breakup and wars of the 1990s.