My main point is such:
Knowledge is a meaningless concept to beyond dimensional beings, if we were to be truly analytical about it. Human experiences, and all our concepts, understandings, emotions and thoughts, everything that defines us as "human" shouldn't apply to a 1-A. As, per defintion, a Beyond-Dimensional Being is unbound and outside everything. Our concepts shouldn't apply to it, it should be utterly beyond recognition. To ask if it is "Omniscient" or not would be laughable.
Yet that is not how it is in fiction.
Instead, many writers treat 1-A merely as a level of power, and allow for Beyond-Dimensional beings to remain fully human in nature and thought. Demonbane makes a clear divide between Elder and Outer Gods, with the Elder Gods being "Heroes of Justice who fight against evil", and the Outer Gods being "The Evil Gods". And Nyarlathotep acts as a teasing trickster ******. It's a superhero conclict, with the Beyond-Dimensional nature of the characters meaning nothing outside of extra power.
Similarly, I/O has 1-A schoolgirls and nurses, and they still act like their limited 3D selves even after their 1-A status. Their minds and natures are still fully human. So again, 1-A is not being treated as it logically should... And that is okay. It is all fiction and make-belief, we should not hold an exclusive law relating to the nature of beings who's nature is beyond our understanding. See what I mean? Arguing to know how a 1-A is would be the same as arguing that you know the "Nature of God". It's ridiculous and arrogant.
Likewise, if a author wishes to write its "Omnipotent" supreme being as being emotional or human, they have all the right in the world to do so. As long as it fulfills our requirements for Tier 0, which is very simple:
"Beings that are boundlessly above absolutely everything, including existence and nonexistence, possibility, causality, dualism and non-dualism, the concepts of life and death, and their analogues at any level."
To be a Tier 0 is to be boundlessly above -1-As. That's it. Levels of Infinity, stomping, feats and cross-verse comparisons are not a part of the debate, and never will be. We don't hold a lack of Omniscience as being a weakness in any other Tier or level, so it shouldn't be one for a being who could theoretically do "anything".