The Great Darkness seems to be some kind of ultimate mutually assured destruction weapon that was deployed in the distant past. Something to that effect anyways. The 'hot zone' as Battuta called it would be the once-livable material universe in its entirety, now infested with a civilization eating superweapon trawling the ashes. If either Humanity or the Vasudans progress to the point where they can be attacked by this entity, the ramifications are somewhat unclear. Perhaps it will simply murder all of them or perhaps it will do something with them that nobody wants to have happening. I would guess something akin to the latter, given how keen the Vishans and Shivans are on preventing anyone from progressing too far. If the Great Darkness just murdered them and then everything returned to the status quo (slow accumulation of entropy), there would be no need for all the drama. Perhaps it triggers the full activation of the weapon or something, I dunno. Whatever it is, it implies the Brahmans may have committed mass suicide to block the Great Darkness from achieving its full effect, (since they would qualify as a full civilization) hiding away as much of themselves as they could in the Vishnans.
If so, I bet the Vishnans purpose is to either continue the Brahman civilization somehow, or to utterly destroy their enemies. Looks like everybody is dead (good job), and the Vishans are still actively doing things, so I will assume the former. I mean, they could want anything, but the fact that the dawn war lead to such total annihilation implies that there were multiple sides with conflicting goals trying to eliminate eachother. The Brahmans seemed to be super-civilized, so I think its a safe bet that continuing civilization is all they really want at this point.
The Vishnans seem to be actively manipulating the UEF, rather than immediately killing them to prevent them from turning into Great Darkness zombies (or whatever it is that happens), which implies that the UEF is related to their goals somehow. Otherwise, why absorb the risk? So, the UEF is useful to their plans. I don't recall where exactly, but something in AoA mentioned the Brahmans were in the process of dying as they created the Vishnans. Maybe their mass suicide as mentioned above. All of AoA was apparantly an intricate lie to control Bei however, so its not clear how reliable it is. Anyways, its possible the Brahmans were effectively frantically packing a briefcase when they made the Vishnans, due to the whole impending apocalypse time crunch. Also, the idea of the 'summed psyche' kindof implies a crappy vector sum was used to try to store the Brahmans as a whole. This coupled with their interest in the UEF implies they don't have everything they need to resume civilization as it once was. Implicitly the UEF has something that they need, so they orchestrated its rise to power and were planning some final event to harvest the needed stuff.
Except, something went wrong in the procedure. Remember how Laporte and Simms were ranting to eachother on the flight over Luna city, about how their civilization was so fantastic and everything was going so great, and then the GTVA kicked the door down and blew it all away? Remember all of that fancy exposition scattered throughout the game about how especially enlightened the Elders are? I bet the UEF is on its way to being infected by the Great Darkness, if it hasn't begun already. The UEF became so good and pure that it made it to the point where it is now the beginnings of a true civilization, to the point that the anti-civilization superweapon has become a factor. I mean, its a pretty elegant extension of the UEF's characteristics. Furthermore , though this is less likely in my opinion, its worth noting the UEF was part way through some complex interaction with the Vishnans when this happened. A lot of people speculated that Shambhala was some kind of attempt to 'ascend into the summed psyche' to paraphrase. To take that analysis and mess around with it, maybe the Elders are trying to complete the procedure the Vishnans started, under their own power. If they are already 'infected', or are at imminent risk of infection, maybe the summed psyche and Vishnans are directly at risk as a result of this. Thats not all that provable though, and from an intuitive perspective is slightly too grand a consequence to fit in with this universe (the destruction or crippling of the Vishnans). Its fairly likely the Vishnans simply want to purge the infected before they reach the point of being too good.
The GTVA for their part might be fully or partially aware of the full ramifications of the UEF's progression. This might explain why they are so eager to crush the UEF as quickly as possible, and learn more about what Shambhala is. If the situation advances to the point of no return, then presumably the Shivans or Vishnans will step in and annihilate Humanity. Depending on the nature of the Great Darkness' attacks, it may not be possible to be selective and only kill off the UEF. If the Elders are infected, and the GTVA knows it, then they probably want them dead just as badly as any of the other residents of the galaxy. It would explain the eagerness to neutralize them. It could also explain why their society is so screwed up, they are actively trying to avoid becoming valid targets for the Great Darkness. Of course, its also possible that they simply detected alien manipulation and attacked the UEF on assumption. "Whatever those good-for-nothing Vishnans are up to, it cant be good!"
e: Various minor final edits (the final read over after posting found more things I wanted to change)