I don't have much in terms of critiques, both of which are minor, one is more specific while the other is more general.
My specific crit is in regards to small phrasing quirk, I didn't catch any egregious grammatical errors, but there was one line of phrasing in the UNAAC overview in that felt a little awkward.
"… the United Nations Anomalous Activities Committee is the Spartans of international security."
I would just replace 'is' with 'are' I feel like that flows a little better.
My more general crit is one I don't have an exact solution for, as I'm not privy to the subtle nuances of British english, but there could be certain word choices that don't align well with what's typically used in that region. Using the UNAAC entry again as an example-
"…any United Nations initiative that promotes normalcy and peace across the globe…"
From what I understand the more formal word that would be used is 'normality' instead of 'normalcy'. It's a very minor thing, I didn't notice any other words or phasing that stood out, and like I said I'm not an expert on these specifics. I doubt that a majority of the people reading would notice, if any at all, but I thought it might be worth mentioning depending on how "authentic" you want it to sound.
Aside from those two things that detract very little, this is a wonderful revamp of what Pierson originally proposed, MI13 feels really fleshed out in a way that doesn't feel cumbersome or needlessly expository. It was all very digestible, not overwhelming with information, and I attribute that to how everything is structured with their own tabs. The presentation as a whole I think is wonderful and with how everything is written in this very formal, but polite, and optimistic? (I don't know if that's the right word, but MI13 gives off a very wondrous feel that's very dreamlike.) It stands distinctly to having its own identity as an agency when compared with the cold, indifferent Authority.
I really like MI13 a lot more now because of this rework, prior I never really batted an eye at this AOI, but I feel like now it has a lot more to offer. I hope this becomes recognized as apart of the canon, and that I was able to articulate my minor critiques in a way that'll be helpful.
Great work!