This is wonderful so far.
How many people live in the area of the Yellow Sea Authority? I imagine there's a gratuitous amount of craters there to be fair, but there's also a lot of room there for survivors someplace or another.
Yeah, all of the Authorities are still more populated than any of the states that border them - their control areas are just very, very difficult to map. (By this, of course, I mean I'm dying to try it.)
The cheesy mass-media kind of raider anarchism was attempted by many entities immediately after the war, but almost none of it managed to outlast the two-week period after which the groceries went bad. If people are still alive in the Authority Areas, it's because they (and their ancestors) were successful at forming state-like societies. So, many of these successor governments aren't much bigger than prewar municipalities, and it falls to the rest of the world to evaluate which should be protected and which should be subdued.
There is extreme variance in living standards and productivity within the Authorities as well. Towards the fringes, many successor entities are indistinguishable from the sovereign states they border, and it is these which most frequently apply to be removed from UN trusteeship if they can demonstrate a basic level of competence and a good attitude towards the rest of the world. In more damaged areas, adverse health effects are widespread and petty conflicts between successors are still commonplace. The most ruined places of all are marked for intensive reclamation, with new towns dotting places like the American Eastern Seaboard and doing a booming business recycling all the rubble they're built on top of. As OTL, international bureaucrats like sticking to the safe cities and it's these treaty ports which see the highest concentration of UN-sponsored activity from above.
This heterogenity provides an interesting contrast to a rest of the world which is more uniformly developed than ever before - Authority issues will sometimes spill into the popular press (not even the end of the world can take the media spotlight off New York) but a lot of it is just boring technocracy, with a long, gradualistic struggle going on to re-integrate as many ruined areas as possible back into the global system.