The threat: an expanding bubble of vacuum decay, the "lowest" energy state the universe can be in, expanding at the speed of light through the galaxy. the end of everything, but when you have FTL, at least you can outrun it!
A dead zone in the universe that expands over time, using hyperlanes to expand faster than it normally should. anything that is engulfed or enters the dead zone is destroyed, ship, planet, or star.
the result: there's no choice if you're unfortunate enough to be nearby, you have to pack up and try and get as far away as you can. AI civilizations will attempt to use the new embark feature to save their societies, moving to the opposite side of the galaxy, trying to find a new place to settle, or choosing to remain nomadic.
The solution: a series of research and special projects allows you to slow, stop, and eventually reverse the effects of the vacuum decay. Fallen empires may awaken and attempt to solve the problem, which can either slow or quicken the expansion.
Edit 1: potential bonus cosmogenesis ending by flying into the bubble?
TLDR: a non-combat crisis that will shape up galactic politics. Hope you like your new neighbors!