well here's my ideas:
1) Have a system similar to a mix of HoI4's factions and Vicy 3's Great Powers' sphere of influences; there would be 3 types of counties within each faction; the Superpower(USA and USSR) who can influence all nations within the faction, world powers(UK, France, China, maybe Japan or India later in the game) who can have their own smaller spheres of influence within he faction, and minors who make up everyone else. then there's the "neutral" 'third world' nations, they can be influenced by members of both factions until they eventually get pulled into one or the other(or split into both by a civil war).
2) have Stellaris type "Ethos" that reflect a nation's attitude/culture/policy/ect. and nations will interact with each other based on how these line up, POPs within a nation would also have Ethos and if there is enough disunity/conflict between the types of ethos present then civil wars or coups can occur(or maybe just different leadership being elected in democratic nations will make the government drift to match the people)
3) have something similar to HoI4's world tension in the form of the
Doomsday Clock; if it ticks up to midnight then a all out nuclear war is probably inevitable, however nuclear war can still happen if someone thinks they have first strike capability or a significant enough advantage that the war would be "winnable"/survivable. the clock will tick up or down due to a variety of things, mostly revolving around the maintaining of nuclear deterrence/M.A.D., but this will only happen if both sides are aware of the disparity in power; for example if you're playing as Russia and manage to set up those missile bases in Cuba without the USA(or any other western/capitalist faction member)'s spies or intelligence agencies noticing then the clock will stay put, but if they do then your going to need to find a way to fix the balance by pulling them out.
4) technology will be put into three categories; secret(new stuff that only you know, can be shared will allies or discovered by enemy spies but otherwise will not spread to other nations who don't develop it from scratch), military(stuff only in use by the army/navy/air force/government/etc., becomes easier to research as more and more nations acquire and use it), civilian(will slowly spread thought the world). most tech will slowly "degrade" through each category over time, though some things will obviously never reach the civilian level, and if you play your cards right all your best toys will stay a secret for a very long time.
5) spies and espionage should be a big part of how the game is played if you're a superpower/world power, putting eyes and ears in enemy territory while rooting out their attempts to do the same in yours, double agents, spreading propaganda and counter-propaganda both in and out of your borders, and so on will be key to "winning" in the long run.
as for the nuclear war itself, I think it having it's own map mode where you'd set up the strategies using a HoI4 style planer to place your missiles, planes, subs and so on and set their targets in the case of war would be the best way to handle it, after all that's how a real nuclear war would be handled isn't it? the plans are already set in the case of needing to use it in retaliation, and if you want to be the one who starts it then you just need to hit the nice big "launch" button...