I've had this idea for a while now of a Universe where Earth is destroyed but the Cold War Continues on Humanity's new home, based on the Verse from Firefly.
An early point of divergence is the Survival of Salvador Allende and the success of CyberSyn.
No one is exactly sure the cause of the End of the Earth, only that for the two decades proceeding Humanity's exodus the planet was wracked by increasingly devastating volcanic and seismic activity. In the 80's scientist across the globe began looking for a place to flee, to save even a fraction of humanity from the intensifying devastation.
The System was discovered during this period, a massive compound Solar System consisting of 5 giant suns orbited by a dozen proto-stars each in turn orbited by nearly a hundred planets and twice as many moons.
News of this discovery led to the race to send Humans to The System. Three projects began development under NATO, The Warsaw Pact, and The Non-Aligned Movement. These massive vessels were built over nearly a decade a assembled in Orbit. An agreement was made to limit the number of original colonists of each ship to 10,000, with more ships to come in the future. No more would ever come.
The technology of the time meant the journey to The System would take about 57 years to complete. Generations would be born and die aboard the ships, never to see The System. The worlds that each ship finally touched down on were inhospitable worlds with only the ingredients for one day supporting life.
The original shelter of mankind in The System was made of deorbited pieces of their original ships, the hab blocks, reactors, hydroponics and more forming the original Arcologies on the worlds. Here the long work of Terra forming began.
For the next 300 years Humanity explored and expanded across The System. the new home worlds of Unity (NATO now known as the Union of Planets), Rebirth (NAM now known as the Rebirth Accord) and Cradle (Warsaw Pact now known as the New Peoples Republic) were turned into Shirtsleeve worlds requiring no survival gear. Each faction began colonizing other planets and moons in The System, while each of the large asteroid belts surrounding the home worlds became home to large "belter' communities.
Each faction maintained contact with Earth despite the decades their messenger probes took to reach Earth. Conditions on Earth continued degrading with more and more sporadic communication until 280 years after arrival the last probes to ever arrive from Earth spoke of Apocalypse and Upheaval. This began the "No-Contact" Era becoming year zero of the standard calendar.
Around 70 NC each faction had made contact with the other two. While originally met with celebrations on many of the worlds of The System, this would be the beginning of the competition and strife in The System.
Thank you for reading my Infodump , if you have any questions or comments they are welcome.
That would especially tie in if you had project cybersyn pop off I feel. And it would give a strong reasons for thr power war powers to still be flopping around like you said