Canonically the Warp just stops a short distance out from the galaxy. It's basically a bubble that envelops the Milky Way. It does canonically protrude into other realities as well, but does not appear to connect to anywhere else in the 40k reality.
As for what exists beyond the Milky Way, there's 2 separate implications.
The first is that the rest of the Universe, or at least the nearby galaxies, has largely been eaten by Tyranids. They've approached from most angles into the galaxy, and it would make sense that they wouldn't extend their traveling distance unnecessarily if they all started from the same point of origin. Most iterations of the Tyranid codex mention this in some fashion.
The other is that there's some piece of canon, I forget where it's from, that says that Imperial probes sent into the void beyond the galaxy have detected nothing but Ork signals, implying that Orks have spread far beyond the limits of known space. Or possibly that there just happen to be a number of Ork vessels drifting lost in the void. I suspect this is from before the Tyranids were a thing.
Given the way the fluff has developed over the years the former theory is the most likely, with the latter being more or less impossible nowadays. As it stands most nearby galaxies have probably been eaten by Tyranids, and they are now converging on our galaxy, lured by the Astronomicon. The Warp is located only in our galaxy, and is somehow linked to the presence of sapient psychic life.