Reading across a ton of space operas, I've seen 'galactic soul' get tossed around in a few distinct flavors. Sometimes it's literally about a cosmic consciousness—like the Mule's mental influence in 'Foundation' or the Weird in Alastair Reynolds' books—something vast and ancient that binds the galaxy together. Other times it's a more poetic, internal thing for characters: the feeling of insignificance against the void, but also a weird sense of belonging to something bigger than any one planet. That ache to explore, or the existential dread it brings, that's the soul part.
For me, the most interesting use is when it becomes a cultural identity. In something like 'Dune', the Fremen have a soul tied to Arrakis, but the Imperium has a galactic soul of politics, religion, and economics. It's less about mysticism and more about the shared fabric of a million worlds, the common thread that makes a spacefaring civilization feel like a single, breathing entity, even when it's fracturing.