I’m from the Laniakea supercluster. And you?
Well, I hail from the Boötes Supercluster myself…
Any game where the location of your galactic supercluster is actually a significant data point is what I would call a high-powered Traveller game.
Thanks to the YouTube videos of Isaac Arthur, I can just grasp what a proper galaxy-spanning Imperium would be really like…
(assuming it has suitable galaxy-spanning jump drives, like those described in Allen E. Johnson’s fine GURPS JTAS article “Across the Galaxy”. You can still find & buy the article at Warehouse 23’s GURPS Traveller: The Best of JTAS, Volume 1: a preview of the books’ contents can be found here.)
…for one thing, they are going to be using an immense number of purpose-built habitats, with only a few quadrillions of sophonts living on rockball worlds.
But I don’t have a single clue how to envision a multi-galactic, galactic cluster, or supercluster-spanning Imperium.