Granted, why we're discussing Eternity, Death and the Endless in a Lucifer vs. Chaos King thread makes little sense to me. After all, you yourself pointed out the tenuous nature of ABC logic. Every step we take that is further away from the characters that are actually in this thread only drives home the point to me: if the feat isn't obvious on its own, within the four pages of the published issue it appeared in, and there's nothing that 100% prevents the feat from being universal, then it's probably universal in scope.
That underlined point is the important part. Crisis on Infinite Earths makes no sense whatsoever if you try to confine it to a single universe. Same with Abraxas. You saw the alternate realities/characters clear as day. With Lucifer and Chaos King, it doesn't render their storylines absurd if one were to interpret it as being confined to a single universe. The story could work.
So when the story can work that way, the loaded term, "multiverse," being dropped has little significance with either Lucifer or Chaos King. Why? Because there's an exponential infinitude of difference between someone annihilating a single universe, and someone annihilating every single alternate universe in existence. And elevating a feat/artifact/character into that exponentially higher tier through a patchwork of character statements, ABC logic and reverse-projection of scenes from entirely different comics is just flimsy. It strikes me as more about wishful thinking than anything else.
Sure, there's an argument. It's just a flimsy argument. Like all the White Crown of the Phoenix and "IG>UN>Multiverse" arguments I've had in the past. And based on what I've seen from both sides here with Lucifer and Chaos King, they're equally flimsy.