Seem to be mostly classic factions actually, with a couple of name changes.
The Athar, Bleak Cabal, Doomguard, Fated, Fraternity of Order, Harmonium, Mercykillers, Society of Sensation, and Transcendent Order are all classic Planescape Factions, up to and including seemingly having their pre-Faction War Factols back.
The Heralds of Dust are simply the Dustmen under a different name, still running the Mortuary under the same Factol.
The Hands of Havoc are presumably a renamed Revolutionary League, possibly with a dash of the Xaositects mixed in - same ragtag bands of anarchists that want to tear down established power structures, but seemingly actually have some ideas about what to put in their place rather than just deferring that discussion into the future in perpetuity.
The Mind's Eye is the real odd one out, as it was originally a post-FW Faction, made up of a union between the Believers of the Source and the Sign of One.
No Free League it seems, but they'd be among the first to tell you they're not really a Faction.
That said, rather than simply the sum total of all Factions in Sigil (and beyond), these twelve seem to be the "Ascendant Factions" that have a significant role in city governance, implying that other, "lesser" Factions (presumably where the Fixers, Incantifers, the old-school Sects, etc. have ended up) are more permitted in Sigil proper than they used to be.
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