Nuclear retaliation might take 20 minutes. The diesel UPS will last that long.
What would the aftermath look like months or years later, though?
Big coal power plants might be targeted, but most solar panels will continue to work; those can run shortwave radios for decades, giving you transcontinental and intercontinental logistical coordination capabilities Duke Huan of Chen would have sold his soul for. Moreover, a Bitcoin transaction is a few hundred bytes; if a backup of your private keys survived on your phone, you can transmit money to anyone anywhere in the world who promises to send you a nice F-14 or two.
> "smelt iron" with what - coal maybe! Now you've got wrought iron, which is good for what,
Essentially all of the iron and steel in the world today is smelted with coal, just as most of it has been since the Song Dynasty switched their blast furnaces over from charcoal to fossil fuel 900 years ago. Modern minimills can of course produce higher-quality steel in electric arc furnaces, but they must start with iron. But there's a huge quantity of iron around; we aren't going back to using knives as money anytime soon.
> "Make gunpowder" - for what, other than to blow up any remaining local PRC leaders.
The tactics and strategy of the Warring States Period are inseparable from the weapons of the time. Even a small Haber-Bosch plant is sufficient to produce enough cordite to annihilate any army of antiquity or even medieval times. Any "warlord" who manages to organize such a thing in the months or years after a putative collapse would hail from the current power structure, which is to say, the Chinese Communist Party.
> "surveillance satellites"? where do you download data? Why?
The tactics and strategy of the Warring States Period are also inseparable from the reconnaissance technology of the time, which didn't even have cameras or telescopes, much less quadcopters, radio-controlled planes, helium balloons, bottle rockets, submarines, SR-71s, and surveillance satellites. No state which didn't have access to such things would be able to resist conquest by those that do. Even NOAA GOES imagery, which is transmitted unencrypted and routinely received by amateurs, would be a decisive strategic advantage over armies that lacked it.
> Most PRC command structures would be smoked.
It seems unlikely that the organization that defeated Japan alongside the Kuomintang, and then defeated the Kuomintang, is as incapable of contingency and succession planning as you seem to think.
> no diesel/gas, no repair facilities and no roads
You can blow holes in highways with atomic bombs; Tsar Bomba's fireball had a radius of 3.5 km, so it could probably interrupt a highway for a few kilometers. But you can't destroy a whole highway, much less all the highways across a whole country; not even the US has enough bombs. Similarly, you can't destroy all the diesel fuel or all the repair facilities in a whole country with just nukes.
What you can do is kill a lot of people. But you probably can't kill everybody in China without killing most of the people in allied countries as well: not just Taiwan, but Japan, Mongolia, Pakistan, India, Indonesia, and plausibly most of Europe as well. Even then, it's likely that hardened facilities would survive.
> The PRC might survive somewhere but more likely would be snuffed out by the people, who would not appreciate the war the PRC had brought upon them
Did this happen in the Battle of Britain, with unappreciative British citizens blaming the Queen and Winston Churchill for the war they had brought upon them? Did it happen in Pearl Harbor, with the Hawaiians booting out the US Navy that had brought such a bombing upon them? Did it happen in the US occupation of Japan, with the Japanese populace angrily ripping Emperor Hirohito and his generals limb from limb as punishment for bringing American nuclear war upon them? Did it happen after 9/11, with the American people snuffing out George W. Bush's government? It's really unusual for a population to side with foreign invaders and bombers against their own elites.
More to the point, "snuffing out" a group requires organization and discipline. An army can do it, and a police force might be able to, but for "the people" to do it, they need some kind of organizational structure, which prioritizes and coordinates the snuffing. Guess what the organizational structure of mainland China is?