That chart sums it up, yeah, but essentially "Litverse" or "Novelverse" are common names for the set of interconnected novels that kicked off with the DS9 Relaunch. A significant percentage of the books since then have been in continuity with one another (and some older novels have been retroactively tied in as well, such as Vendetta or the New Frontier series), referencing one another and making effort to be consistent with one another, forming essentially a Star Trek EU.
Update from Patterns of Interference: the Ithenites joined in October 2165 as the tenth member of the Federation. The Tesnians, Xyrillians, and Lorillians all considered joining, but declined for various political reasons in the aftermath of the Partnership incident.
Last Best Hope paints Andoria, Earth, Tellar and Vulcan as the Big Four. Apparently, Alphacent isn't a founding member in this continuity? Also, Mars is devastated in PIC. That's a major thing to happen to a coreworld - unless the new continuity only treats Mars as a colony instead of a Federation member in its own right.
It's the same canon continuity as before, allowing for the fact that said continuity has been in constant flux for more than half a century due to being fictional and all. It was never actually canonical that Alpha Centauri was a founder; Enterprise only mentioned the aforementioned "Big Four." (It was mentioned in a nigh-illegible article in Generations, but that doesn't really count.) Still, those being the most prominent worlds as of the 24th century doesn't preclude AC being a founder; it could just mean that it's been eclipsed in importance by the other four. After all, a lot can change in 220 years.
I mean, canonically, Alpha Centauri has never been established as a founding member. ENT's "Zero Hour" talked about the founders, but it framed them in terms of species rather than in terms of planet or planetary state: "Humans, Vulcans, Andorians, and Tellarites." Which left the door open for the Litverse to establish Alpha Centauri as a Human-populated fifth founding state. DIS's "Will You Take My Hand?" had scenic art that implied founding roles for Earth, Vulcan, Andor, and Tellar through the use of their respective emblems at the Federation facility we saw in that episode, but it didn't use any art to imply a role for any other Member State, including Alpha Centauri. As Christopher noted, though, there's probably still room for us to imagine that the Alpha Centauri Concordium was a founding member if we presume it's been largely eclipsed in political importance since then. Well, the canon has never established Mars as its own separate Member State. The Litverse has, but the Litverse has also always implied that the Confederated Martian Colonies has always had less power and influence than Earth and has resented its second-tier status. The Romulan War duology referred to it as the "cosmic Canada." (The Litverse has also never been able to settle on a single name for the Martian legislature -- Beneath the Raptor's Wing referred to it both as the Governing Council and the Assembly, while Section 31: Control referred to it as the Martian Parliament.) This is consistent with how Mars is portrayed in PIC, actually; the entire planetary surface looks to have been devastated, but there were only around 92,000 deaths. If Mars had achieved a level of power and influence within the Federation on par with that of Earth or Vulcan, we would expect a population somewhere near 5-10 billion. I would hypothesize that Mars probably has a much larger population underground and/or in domes that managed to escape destruction, but its population has probably always lagged behind the Earth/Vulcan level. The attack on Mars was a pretty psychologically devastating thing for the entire Federation even if Mars were only an Earth colony, though -- an entire planetary surface got bombed deep within one of the Federation's core systems. If someone managed to blow up Liberty Island but wasn't able to touch Manhattan, that would still be a major psychological blow, after all.
Yes, but having a planet is not the same thing as that planet being a Member State. Planets can part of a larger Member State, the same way Long Island is part of the State of New York instead of being a state in its own right.
I confess, I always wanted to see the Ekons and Zeons join the Federation. THAT would be an interesting follow-up to "Patterns of Force"
I always imagined that Zeon would join first, and it would take a lot of time to help Ekos recover from the Gill-Melakon years.
It's also possible that worlds 'within' Federation space remain independent over resentment over an earlier contact. Eminiar and Vendikar maybe.
I imagine that they wouldn't be in Federation space per se. Federation space probably ends at the edge of their solar systems; they'd be surrounded by Federation space but not in Federation space. Kind of like how the territory of the Kingdom of Lesotho is surrounded by the territory of the Republic of South Africa but not in the Republic of South Africa.
Yep, that's why I used quotes around within. I'd guess the UFP soft touches them, hoping they will eventually join. In the meantime if a ship leaves its system a Starfleet vessel will escort it, but not intervene unless necessary.