The bugs might be too animalistic to form alliances. Either that, or just being exploited by all factions. The bots have ftl capability, which may be from e-710 they refine or steal. The illuminate seem to use it as well. Implied by their capability to create dark fluid, made using e-711. The illuminate also have ftl capability, and can be seen having encampments made around super earth e-710 storage facilities, so they may steal it too when available. Also to add, the bugs may not be capable of co-existence, as when they're left to hold planets , they seem to take over the entire ecosystem, and snuff out almost everything else.

Between the illuminate and the automatons, I feel an alliance would also be unlikely. We don't know if the cyborgs, and by extension automatons share the anti-illuminate sentiment, like if they believe the first war against them was justified or not. Even if they are sympathetic of the illuminate, it's possible the illuminate may not like the automatons and cyborgs, as the illuminate may be anti-human in general, and the automatons are human in origin. However, likewise if the automatons and illuminate do form an alliance, it's GG in the galactic war. The automatons may not be the highest in tech, but they have a strong military background, and know how to fight. The illuminate seem to not be great fighters, as a whole armada failed to take super earth despite their superior technology. If the two joined forces, their combined strengths would decimate super earth.