Most of these are not 'new', just expanded.
The ones that fit right into the existing armies are bloodbound(warriors of chaos), sylvaneth(wood elves), everchosen(warriors of chaos), ironjawz(orcs and goblins), and tzeentch arcanites(warriors of chaos and daemons of chaos).
So those just fit in already to the existing armies.
The only 'new' ones are stormcast eternals, fyreslayers, and kharadron overlords.
The SCE would pretty much have the exact same story and origins. Sigmar takes up souls from battles, and reforges them into demi-god warriors to fight for the Empire and any other forces of order. They are not battle automatons, as said, but great heroes with physical bodies and magic weapons and armor, given a second chance to eternally fight against the unstoppable chaos hordes.
Fyreslayers would not necessarily be linked to the slayer cult, but would be another faction of neutral dwarfs, sort of like how the chaos dwarfs are, but not chaos aligned. At some point Grimnir comes back to fight a great adversary and dies in the fight, but killing his foe anyway, and his remains are scattered all across the world. This gives the fyreslayers a motivation to hunt for these fragments of ur-gold, still hammering it into their flesh to gain the power of Grimnir. I don't see a reason much would change. They do not need to be slayer-cult, that can still be part of the main Dwarfs.
Kharadron Overlords would be a separate faction, but an offshoot of the Engineer's Guild. I would probably drop the aether-gold thing, because that is pretty much a mortal realms thing, but they could still have found some other means of levitation, and their main goal is profiteering and merchantery.
I honestly do not see this happening, but I can play along. I actually happen to love AoS and the direction it is going, but I do fantasize about the new factions and models fitting into the old world.