AFAIK new eden is a globular star cluster of the milky way galaxy. so omega centauri, pyxis, or any of the other 150+ known globular clusters in our galaxy (or just a made up one)
If we ignore that in the real world globular clusters are generally low on the elements required to form planets, most everything else about them makes a lot of sense for eve. Low hanging fruit, eve is often called a cluster. but going beyond that, the average star cluster is only about 100,000 stars, which means that at ~5000 systems roughly 5% of the cluster is connected by stargates. so fairly well colonized but still leaving plenty of room for “boring” or “un-profitable” stars that no one ever bothered to connect with.
Globular clusters are also much more dense than the rest of the solar system, with the cores of some clusters having seperations between stars only about as far as our solar system. now obviously the eve cluster isn’t QUITE that dense, but when you compare it to the main milky way they are practically crammed in there.
For reference, there are only 12 or so stars within 10 light years of earth. Choosing a semi-random system in eve (I went with osht in curse because the name amuses me) there are 372 systems within 10 light years.
Finally, globular clusters are somewhat seperated from the rest of the galaxy, they still orbit the galactic center so are still “part” of it, but there is generally a band of rather empty space between them and the rest of the galaxy (not completely empty mind you, and some are closer than others. but relatively speaking). which would explain why none of the 4 races have ever tried to expand beyond that cluster. since even sending a ship out there at the highest warps they can manage would still take hundreds or even thousands of years (assuming they can even keep their warp engines going for that long) just to reach the galaxy proper, and even then there is no guarantee that a gate network could be set up over those kinds of ranges.
so its likely that the empires of eve are aware of the rest of the milky way galaxy. in much the same way that we are aware of it. but likely pay even less attention to it than we do, since, being so distantly separated from it its unlikely that they would ever be able to reach it anyways making it more of a mild scientific curiosity until technology develops further (and they have bigger things to worry about)