> How many stars are within 100,000 km of each other and what percentage of stars does that represent
That's less than half the distance from the Earth to the Moon, so leaving binary star systems to one side, the answer is none and zero.
A large asteroid passing 100,000 km from the Earth is a considered a near miss in my book, since it's easily cislunar.
But you're missing the point entirely; parent is saying that individual craft in the swarm are within that distance of each other - that's the diameter of the swarm; the line "The swarm ends up around 100,000km wide" gives that away.
The distance between stars is orders of magnitude larger. "the swarm" crosses interstellar distances and communicates back as a whole. But communications between elements of the swarm do not and cannot cross that distance, they have to stay quite close to each other, e.g. within 100,000 km as they cross the void together.