Imagine intelligent life arising on a planet around one of those stars. I wonder how long it would take their astronomers to figure out where they were.
This would be an interesting premise for a science fiction story. You could imagine a species realizing that the only way to survive long term is to keep hopping to new star systems every billion or so years. And when they get ready to hop to another system for the first time, they realize almost all the viable star systems are already colonized by past species who came to the same conclusion
Greg Egan’s Incandescence is along these lines except replace star in the trail of a black hole with asymmetric asteroid around a black hole accretion disk.
I read that, but have either forgotten, or missed the entire black hole thing. I think, for any given Egan novel, I miss about half of the ideas while trying to wrap my head around the other half, but he's still one of my favourite authors.
Would there be a similarity of stars? We see lots of stars because we are in the middle of a galaxy, but they are outside of a galaxy. They could see the galaxy they came from in parts of their sky, but would it really be like actually being in the galaxy? I'd imagine not. It might only be visible from one hemisphere of the planet, depending on how the ecliptic was aligned. The other hemisphere might only see black, with maybe one or more moons and other planets.