I disagree that the Chaos God exist outside the Milky Way. For one thing, the Deep Warp is a thing, and that's a "place" where even the Big Four fear to tread, so the known Warp is at the very least limited in size, if that is even a word that can be used to describe it.
The Deep Warp is not a thing. Well, it is, but not what people say. The Deep warp is mentioned in a single book, Path of Heaven, and its not a super hyper spooky place in the warp.
People mistake it with the Well of Eternity, and sometimes the Aetheric Void from Age of Sigmar.
Secondly, the Tyranids are extragalactic, yet they caught the Chaos Gods completely by surprise, and neither side seems to have been aware of each other's existence.
They dont, they got chaos marines on surprise, but nothing indicates the Gods arent aware, we dont got their pov after all. We know from Devastation of Baal that the only thing the Hive Mind finds strange on this galaxy is the warp bleeding into real space, indicating warp rifts are rare.
Also, if the Chaos Gods were truly nearly omnipotent and omnipresent, they wouldn't be scared shitless of the God Emperor.
When the 4 blessed Horus he had effective infinite power, and easily beat the Emperor. But that was on real space, where they cant use their power without a vessel.
A tornado releases more energy than a nuke, but a tree can survive it, since the way the energy is released is different from a nuke. They got power, but cant cross the barrier or concentrate.
(...)wouldn't they be able to bring xenos from elsewhere to aid them in their fight here? (...) Granted, Chaos Space Marines aren't exactly in the habit of sharing stories with their cousins, but we've had a lot of material from their perspective, and yet at no point was ever an individual or group seen traveling outside the Milky Way, nor do they ever mention seeing anyone else doing it.
Not at all, in fact we got a Chaos Marine talking about his trip to the void beyond the galaxy in Lords of Silence.
Besides, GW barely talks about xenos, as far we know, they do, but those arent space marines or primarchs, so they will get no content on a chaos army.
Older lore stated that Chaos was multiverse, this is how WHF could get crossovers with 40k.
Newer lore doesn't know and just avoids making a statement, everything is canon.
On the oposite, newer lore is even more explicit, all the out of universe comments by White Dwarf on how daemons and the warp are the same, how Slaanesh was indeed created by the eldar and in fantasy it got interest on the elfs because of it, came from 2017 onwards.
"Everything is canon, not everything is true" is a quote that the fans dont got, Laurie said when he was the IP manager that it just mean the lore is maleable and so new things take precedent, like how on Bungie times officially the lore from the Halo games is more important than the books, so if new information comes (like the Halo Reach game) it takes precedent (like all things that contradict Fall of Reach)
Now, if you ask me, I dont like it, and neither like the idea GW consistently pushed since 1993 that if the Emperor dies, the entire universe dies with him. By making chaos a force with infinite realities to feed, they are just invencible, the Necrons and Tyranids wont outlive the universe, but Chaos will a trillion times over.
I personally like the idea from War of the Krork, where chaos is multiversal, but not the gods. Chaos is a natural process of any universe with a warp, there may be another god of war just like Khorne, but its not Khrone, the same way a storm on Earth and Neptune arent the same.
