The Mongols were technically advanced, they were just not very urban. They had one of the most impressive pre-industrial mail systems in the modern world, and they are largely responsible for the sudden spread of gunpowder weapons. The problem was that not being urban also came with not being politically stable, and their culture was so ephemeral that they just sort of got absorbed by the people they conquered.
But regarding FTL, the circumstances that would make it easy also have significant implications. Consider the amount of energy, and the mastery of the physical world, that would be required here. We're talking about a society that can harvest solar power straight from the source, and who's idea of a super-weapon would be one that destroys entire solar systems in a single flash. They would live in a world where human labor is viewed the same way we view stone tools, and who can manipulate their own genes and bodies to achieve near immortality. The culture and stability of such a society would both be difficult to understand from our perspective. And the thing is, what I am describing is probably just a near-galactic civilization. I don't know if I can fathom what possibilities lie beyond that.
Which isn't to say that it is impossible. Just remember that, with multi-galactic civilizations, you are dealing with demi-gods.
Perhaps looking at the way the Greeks saw the gods may be of one way to do so. They were immortal, didn't have manual labor and pretty much were custodians of the world who intervened frequently in human affairs and had shit loads of infighting. So it's definitely not impossible, but what you describe pretty much sounds like the cap of how advanced you should go for some reason. Like, they still sound bound to reality in a way the entities aaron describe aren't.
As for multi-galactic societies I actually have imagined a couple if you're curious. Both of them named after super cluster groups for the sake of it. One is the Leo, who are that aforementioned endless swarm of drones that have colonized multiple galaxies. But even they probably are orders of magnitude more advanced simply because it's not hard to imagine these drones using star lifting to increase their populations to cover whole galaxies.... There'd be more of these drones than there are grains of sand on earth.
The other are the Virgo, who pretty much ran into a similar issue Aaron brought up; they are so advanced they don't even exist in reality anymore, instead having become part of it. Hard to really tell a story from that sort of perspective.
But the thing is i'm not thinking of multi-galactic pan-cluster entities. I'm only thinking of societies that can go to the Andromeda and not much further. The local group is a pretty tiny compared to the rest of the universe. Is the jump in tech to get to other galaxies just that big? If I just say the FTL you get when you figure out how to make a warp drive is just that good, would there still be problems?