Starfire does not track radiation and dust. What matters is how many population units survived, and of course the shipywads my impression is that a signifigant amount of the population will have survived as most of the bombardment seems to have been aimed at PDC's with a few other salvo's at population.
However even assuming I am right that will have reduced the production of earth a lot and so hurt the human economies. The shipyards are probably less critical in this situation as a lot seem to have survived and the ability of the humans to maintian their fleet has been reduced so they can't afford to build a lot of new ships
You are right, about half the shipyards survived, as the Coalition never targeted the Russian yards. However, you are also right that the yards are not the biggest consideration right now. The Coalition in particular had about as big a fleet as it could support, but the Russians were behind them because of their losses. The surviving fleet will have to worry first and foremost about maintenance. Both fleets have some maintenance set aside for support for planned offensives, but certainly not enough to keep them going for long without the support of the civilian economy, or what is left of it. And both sides have the problem that neither government ever set up sector capitals or anything like that, so in essence the governments of both were concentrated on Earth. The Coalition was close to setting up two different sectors in its colonial territories, but the war intervened and it never happened.
The rules don't really cover this, except for covering setting up replacement capitals if a race loses its original capital, so I have to role-play this. And I see no reason that either side's colonial territories would remain a unified whole. In the Coalition, there are two factions, set up around the two main warp chains, Epsilon Eridani and Sligo. They both have different outlooks and will react differently to the disaster. Its more complex for the Russians. The Tomsk Union is already independent and that will not change. Most of the rest of their colonies are occupied by the Rehorish, and so have no opinion until liberated. The USSR's remaining colonies in the Moskva system are its oldest and most developed, but it is still just one system with two inhabited planets.
Admiral Ruston and General Semenov need all of the colonies to support their fleets, or they will have to mothball most of their units within a matter of months. They will argue for a unified front against the aliens, but they also have to deal with the current war and with the chaos and mega-deaths on Earth. Fortunately, they have a lot of respect from the people of the colonies, largely because they stayed out of the conflict on Earth and put the needs of the people outside the solar system before the mess on Earth.
Kurt