To clarify: Sync starts in 2364, and after the jumps to the empty systems and back, time has elapsed three years, leading up to the beginning of the SSI with the destruction of the Vigilant. The Persistence engages its drive, and, instead of transporting itself across vast distances, simply sends itself some time into the future. It traps Phi and Omega, but heavily damages them in the transit, however leaving the other ships untouched.
The red nebula at the end = Capella post-supernova.

I'm not entirely sure whether you are presenting that as
fact or
theory. Either way, I'm about to knock some holes in it.

Where did you come up with that "jumping through time" idea? The final jump that Sync initiated appeared no different from the other Sync-jumps; there was nothing there to suggest a temporal-jump.
As for the red nebula being Capella, that just isn't feasible.
#1. The sun in the nebula was
red, along with the rest of the nebula, and furthermore was a
full-sized sun, not a neutron star, as Capella would have been turned into (it wasn't nearly large enough to form a black hole).
#2. There was a Knossos portal in that nebula, leading right into a Terran-occupied system. Since when did Capella have a Knossos? And how did said Knossos survive the supernova? Shivans don't build Knossoses out of Ancient materials...
#3. Any post-supernova nebula would be ridiculously hot, and wouldn't cool down for several hundred million years. Unless you're seriously suggesting that Sync time-jumped them
that far, which it didn't, as evidenced by the Terrans using FS2-era tech at the end of the campaign.