Sidenote: I sincerely doubt that the Shroud has any actual link to the Unbidden.
The Shroud isn't a physical "place" from what we've been shown- its more of a realm of consciousness, populated by thought-entities. The Unbidden, however, are quite "real"- they're extradimensional, something we see plenty of other places in Stellaris.
Furthermore, the Unbidden are attracted by Jump Drive technology, not psionics.
No... I suspect that the End Of The Cycle is a more... insidious threat. Something new, certainly, and not just another way of triggering the most over-represented Crisis in the game.
Consider: what's scarier, getting a massive boost to production for 50 years and then needing to throw the doomstack you've built with it at a portal, or, say, your entire empire's populace suddenly gaining the "neutered" trait?