The US and the Commonwealth just took Europe to pieces, including the (it will likely later be considered) murder of 6 million+ civilians and permanent destruction of the German state using biological weaponry. Three-quarters of the population of what would later become the developed world IOTL, and was formerly one of the most developed areas of the planet both ITTL and IOTL, has been reduced to squatting amidst the rubble praying that the shooting will stop soon. That's the lucky ones. The unlucky live in Germany proper and many will starve to death before war's end; the truly unlucky are dead of anthrax. Europe is not, and CANNOT POSSIBLY become, the stable major economy we know and take utterly for granted today. It is, arguably, worse than Africa today, and its psyche even more profoundly scarred.
In Asia, there is not ONE functional nation-state north of the Himalayas. NOT ONE. China will fall into civil war the millisecond American aid is withdrawn, Russia exists only to keep Molotov alive, Japan has been reduced to near-medieval conditions, Central Asia has been raped by Germany, European Russia might as well not be there at all. The sole functioning countries to be found in Asia are to be found in what will soon be the former British Empire and possibly the Philippines.
Africa is, as IOTL, a crapsack.
There will be no peace; there will be civil wars in Asia and Africa that a more proactive UN will send American, British, Indian, and Latin American soldiers to try to end. There will be violent terrorism, guerilla warfare, armed resistance, and ethnic terror in Europe, that American, British, Indian, and Latin American troops will bear the brunt of. There will be continual and draining conflict everywhere in the world outside of the Americas, Oceania, and the few select states in Europe that have remained neutral and weathered the storm. Europe will be occupied for three generations, and there will be blood as we feared there would IOTL.
No, no one can or will challenge American-Anglo (and eventually Indian and Brazilian) supremacy over the world, but they'll set upon each other for every conceivable reason; the steps the UN takes to restore order will be shaped in the mindset of total war, and will be ultimately counterproductive. The world of the next century will be dominated by the idea that the village must be destroyed to be saved. There is no hope for a quick and easy redemption; while Americans (likely used in the sense of "Denizens of the Americas), British, and Indians will come to have much the same standard of living enjoyed by Americans, Canadians, Japanese, and Western Europeans today, they will live in a society perpetually fighting a low-grade war to maintain order over a still-broken world that heals only slowly.