It's important to note that the Archive's purpose is not to store information. Its purpose is to feed stories to Beholding, and it's organised primarily to do that.

So what happens is you write down your story. The presence of the Eye forces you to write it as a story- here, analogous to the cooking, I guess. Forcing you to put it in an easily digestible manner. It is sent to the Archivist, who here works as the Eye's "mouth", and they read it out. This feeds the story to the Eye. You can also give a personal statement, which will be recorded, but this is a bad idea.

The researchers, who in this analogy are the Eye's digestive system, go out to analyse the story. They rule out ("vomit up") any hoaxes or mistakes or other indigestible meals. As for real statements, they find any lingering fear- "No-one can explain how, in a building that size, he spent the better part of three years alone except an old wooden coffin", that kind of thing- and add it to the statement. The story is now fully consumed and put away in the archives, the Eye's "stomach".

Everything else- the library, the scientific contacts, artifact storage- they don't do shit. They're only here to give the illusion that this is a real scientific institution rather then the gaping maw of a nightmare god. They're poorly managed because Jonah doesn't actually care about advancing knowledge.

The institute seems chaotic because it's stated goal is very different from its actual goal. Seen for what it is, it's organised just fine.