All those people at the end are the multiverse's tourists and are looking at the newest universe integrated into the multiversal community. They aren't some great hope, they're just sightseers interested in yet another "Nazis win" timeline. No accounting for good taste. As a pragmatic concern, there's a policy of non-intervention among the major states which interest themselves in human affairs, and while that is sometimes violated, there's already numerous temporal cold wars going on already.
The American Reich conquers the defenseless Western States. Did you really think that an entire empire is going to disappear because you got rid of the top guys? There's an entire machine of death in place there, one that's already killed millions of people. It's going to continue on, even if some top brass are dead. They'll also conquer as a means of asserting themselves as the third superpower in the world, capable of speaking to the Third Reich and the Japanese Empire as an equal. Plenty of whites in the former Pacific States join the American Reich. The BCR and Azatlan are wiped off the map.
Dissidents and would-be resistance are enticed by the opportunity to escape to other universes, some of which are not tethered to the local year. Why eat mice in a basement hiding from the SS, when you can find a universe of nothing but endless beaches? This incidentally acts as a release valve for the three superpowers, who offer permanent exile as a carrot/stick for resistance movements. The American Reich even offers "National Socialism with a human face" by forcibly deporting "undesirables" to "interdimensional homelands." The idealists who stick to it and try to fight are now even more outnumbered, and are brushed aside.
Japan lets go of China, save for Manchukuo and the treaty ports. They then realize that the rest of their empire is easier to control now that they don't have to deploy troops across the Pacific or against an endless sea of people. There are negotiated home rule agreements with India and Australia, with Australia immediately leaving and entering the Reich's orbit as a virulently white supremacist state.
The multiversal community sees the nature of the three superpowers and collectively rolls its eyes. You see, when there are infinite copies of everyone, any individual incarnation isn't worth very much. Everyone who's in the know in the multiverse is very blase about the value of life. They've seen countless worlds ruled by murderous regimes, they've seen entire species scoured from one universe but thrive in the next. Many of the major multiversal powers are just as bad, if not worse, than the Axis successors.
After a few decades, High Castle world becomes a bit of a cheap tourist trap. The three superpowers have grown to integrate their economies into the greater multiverse, and have become "blackboxed": their whole economy is dependent on technology that they can barely comprehend, manufactured by factory-world several universes away. Major cities become space age, while the rural areas stay "frozen" in the 1960s. This is deliberate, as the major source of income there is tourists looking for a "quaint" Axis victory timeline to spend a few days before going back to manufacturing plumbuses.
The three superpowers have integrated themselves into the web of intrigue that is the multiverse. It turns out there's an existing group of interdimensional Nazis, and given their infamy among some other powerful timelines, they seek other Nazis and band together. To them, the multiverse is like prison, and they have a gang. The American Reich tried to join other Americas, but got rebuffed, and aligned itself with a more authoritarian Anglophone club dominated by South Africans. The Japanese found other Japans, all of whom are rather insular.