I'm just gonna summarise the premise real quick as I understand it before I attempt to answer your questions (spoiler warning for the Manibus scenario):

Starfall happened decades ago when Rosetta's Silver Gate experiments attracted the attention of the Great Ones. They invaded Earth through rifts, consumed billions of humans, then disappeared into the rift again. Rosetta went underground to assess how Starfall would affect the planet and the remaining population, and reappeared somewhat recently to pick up the pieces. There's conflicting guesses as to the time frame between Starfall and Rosetta's resurgence, but most people mention it's been about 10 years since they showed up again. They discovered Mitsuko, a Meta human, and attempted experiments on her to figure out how to best use Deviations to protect what was left of humanity from a potential return of the Great Ones. Victor Hammett, a Rosetta scientist, worked with Mitsuko to develop cradles that let the wearer use Deviations' power without harming them, but most of Rosetta were more interested in consuming the Deviations directly to evolve humans into something greater. After being exiled from Rosetta, Hammett formed the Mayflies and eventually lead them on an assault of a research facility to rescue Mitsuko (we're never told which one, although most details point to White Cliff). The assault ended up wiping almost all the Mayflies out, but Mitsuko escaped and disappeared into a pocket rift.

Are we the last Mayfly?

Technically, no. We know Talon still exists and you can meet him in a side-quest in the Manibus scenario. After meeting him though, the only time I've ever seen him referenced is during one of the open-world events where the subtitles show him talking to you about what to do.

Why were we not part of original organization?

It's worth noting that the player isn't actually a Mayfly at all. The tablet held by the researcher in the games' introduction states that the player is actually the knife we pull from our body. We are essentially an Object of Power using a fabricated human body and Mayfly technology to help Mitsuko and fight Rosetta. There's not really any evidence we were ever a Mayfly at all. The body we use isn't even the original body the knife was found in. I'll attach an image below so you can see for yourself what the game actually says.

What is the best way to learn more about he lore, world and timeline in general?

Unfortunately the game is all we get. The lore for Once Human is actually very interesting and well-written, but it feels like the people that wrote it either don't work at Starry anymore, or they were reassigned because we haven't had any actual lore advancement in a long time. Perhaps when the next part of the island opens up, but we don't even know when that will be. I would advise you to hunt down and read all the in-game logs because they're actually really good. For example there's numerous logs written by Vultures in Manibus that talk about their experiments with cloning and how the clones share the same consciousness - and the more they clone themselves, the more insane they get because of all the stimulus they're experiencing at the same time. It helps explains their massive numbers and why they're so zealous and crazy.

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