My view of the chronological order of Jinrui wa Suitai Shimashita episodes
(There are some semi-spoilers for Jinrui here, but this is deliberately mostly opaque if you haven't actually seen the show.)
I'll put my conclusion first and then write on about my justifications later. Based in large part on Vance's comment at A&V, my assumed chronological order of episodes is: the school portion of 11-12, 10, the epilogue of 12, 7-8, 5-6, 1-2, 9, and ending with 3-4.
There is a clear ordering of some episodes: the school portion of 11-12, 10, 7-8, and then all episodes with the Assistant (1-2, 3-4, 5-6, 9) in some order. It's strongly implied that 1-2 follows shortly after 5-6, since Watashi's hair is cut at the end of 6 and episode 1 is the only other episode where she has short hair (and she returns to long hair before the end of the episode).
(Although I think the ordering is sensible, I don't think the show supports Vance's logic about the relative positions of 9 and 5-6. In 6, Watashi is rationally afraid because she's around a bunch of angry people who are upset over what she's deliberately done; in 9, her screwup is mostly accidental and pretty much private.)
The position of the non-flashback epilogue of 12 is not clear to me. It has to go after 10 (since Watashi has fairies) and before 3 (since the epilogue is the first time since school that Y and Watashi have seen each other). I think it can't happen shortly before 3 since the dialog between Y and Watashi in 3 implies that it's been a while since they saw each other. Based mostly on Watashi's relative equanimity in 7-8 onwards, I prefer to put it between 10 and 7-8.
It makes both internal and thematic sense for 3-4 to be the chronologically last episodes. In internal logic, 3-4 is where Watashi is the most hands-off and concerned about the fairies and their enthusiasms (an attitude that makes sense for her to have after 9). It's also where the faeries are the most overtly weird and ostentatiously magical in what they do. And, as Vance mentions, it's set in winter or very early spring, unlike all of the other episodes. Thematically, 3-4 can be read as a meta-commentary on the show itself and episode 4 climaxes with the characters' (manga) series being canceled, the characters waking from a dream, and so on. Applications to the end of the anime series itself are obvious.
(Read this way, many of the lines at the tail end of 4 can be given double meanings. Consider Watashi's line that the fairies' mangas are too hard, for example, given that Jinrui itself requires work to understand at more than a superficial level.)
I have no idea what chronological order the original light novels are in and I'm not sure it matters. I'm inclined to consider the anime a separate creation from the LNs instead of an attempt to adopt them literally. (The things I see in the anime may be there in the LNs too, but I'm not assuming that. Jinrui feels like something where the anime may have gone in its own direction.)
A theory of decline
One of the periodically recurring tropes in anime is humanity being in decline; not through a loud apocalypse or for any visible reason, but people are just quietly diminishing. This season's Jinrui wa Suitai Shimashita puts this in the series premise (the title of the show means 'Humanity Has Declined') but there are plenty of others, such as Sora no Woto and the classic Yokohama Kaidashi Kikou. In the version of the trope that I'm thinking of, the cause of the decline is never stated (and the decline itself is often just a background detail, not the main focus of the show). One of the things that this generates is a lot of speculation about why humanity is in decline in any particular show. What catastrophe do the creators imagine having hit us?
As it happens, I have a theory on this. Japanese creators are almost uniquely placed to vividly feel one particular quiet catastrophe in real life: a low birth rate. The Japanese total fertility rate is one of the lowest in the world, well under the replacement rate necessary to just hold the population level constant (see eg Wikipedia). The effects of this decline are apparently visible all over Japan, especially in less attractive areas with lower populations. The whole issue is considered a serious problem (especially when combined with an aging population), with various government attempts to encourage children, discussion in the press, and so on. Extrapolating Japan's very real issue with a low birth rate into a future setting is a natural thing to do.
(As you'd expect, I believe that one of the most visible signs is fewer and fewer schools with fewer and fewer pupils. This has cropped up as a plot point in contemporary shows; for example, I remember the climax of the GTO live action series taking place at a now-shut-down rural school that one of the characters had attended.)
A really low birth rate is a great fit for the typical anime decline of humanity. It's slow but devastating, it's quiet, and there's nothing really to fight or to make a fuss about. There's no singular event that's causing the problem, just a whole collection of small individual decisions. Life goes on, the world shrinks (because there are fewer and fewer people in it), and so on.
(And with fewer people in the world you start to progressively lose technology that you no longer have the manpower to run the infrastructure for. It takes a lot of people all through a supply chain to run a modern chip fab, for example, especially once you include things like the transportation infrastructure, the water supply, and so on.)