The Empress Wave is actually the remnants of a warning, sent by the Yaskoydri to their outlying colonies. When their homeworld near the galactic core was about to be destroyed by a wave of radiation, they created a psionic wave to compel their colonies to pack up and flee, as the radiation wave was sterilizing system after system. There was no dealing with it, just leaving before the radiation arrived, so they wished to prevent their colonies from tarrying in the false hope of saving something. The "Empress" that many survivors of the Wave recall seeing in its message, was the main person who gave the warning - the one the cameras which would broadcast the signal were focused on for much of the recording.
Over many thousands of years, this signal degraded. By the time it reached Charted Space it was an incoherent jumble - but still powerful and panic-inducing, per its original function. The radiation wave it warned about had long since petered out, its energy distributed over the surface of an ever-growing sphere - much of it outside the galactic plane, and much of what remained in the galactic plane absorbed by planets, stars, and other matter on the way - while the Empress Wave suffered much less strength reduction, having been confined (more or less) to the galactic plane and only interacting with sophont minds (thus, completely ignoring barren systems). Ironically, it became a calamity similar to that which it was meant to warn about.
In theory, it may eventually be detectable by sophonts in neighboring galaxies, assuming there are any when it gets there. However, it will take tens of thousands of years - far more the length of time from the first spaceflight on Vland to the advent of the Galaxiad - to reach the nearest galaxies.