Well, the question still remains of "symbiotizing what"? Fungi on earth range from saprophages, which decompose dead matter into nutrients, to mycorrhizae, which form symbiotic relationships with plants which produce nutrients. In either case, they're feeding off of things, it's just the source that varies. All living things need to gain energy somehow.

The mycelial network is spooky and probably feeds off something more abstract, since sci-fi and all that. That said, maybe it's in some sort of symbiotic relationship with the multiverse itself? There's so much energy in a galaxy, let alone a multiverse worth of galaxies, that it's not hard to imagine a fungal network feeding off just a tiny fraction of that energy. And interstellar space has relatively low energy, so it makes sense the network wouldn't build hyphae there.

You're right that they never said it only works in the Milky Way, I had just assumed that since it peters out at the border of the galaxy that it ends there. And if it resumes in another galaxy, it seems like it would be discontinuous and thus a separate organism. But I suppose if you imagine it as a wholly separate subspace realm, with hyphae that connect out wherever there is sufficient "energy" of whatever sort it feeds off of, it makes sense. And jumping to another galaxy could be a cool twist indeed!

~~I would give anything to be an astromycologist~~