EDIT - And, wasn't Seath in the "The Duke's Archives"....
Good point about Seath.
I mean, if you look at Brightstone Cove from afar, you see tons of crystals down in the valley, reminding me of crystal cave in Dark Souls 1, and when you get to the bottom, you defeat "Dear Duke's Freja", which immediately reminds me of the Duke's archives in Dark Souls 1, especially since it leads to a room with a library immediately afterwards, and a primordial bonfire.
In that cave you find a huge fossilized Dragon, perhaps a throwback to Seath. The great soul is not carried by the Dear Duke monster, but rather lying on the room in a puddle of strange energy seeping from the dragon. If you return later, you find that puddle has evolved into a crystal structure, once again a reminder of the immortality crystal Seath had, plus it reminds me of how in DS1, magic, crystals, dragons and immortality were said to be linked. You can enter that memory to see the fall of an ancient dragon, an image that could be a memory from Seath's own genocide of his own kind.
I'm getting the following vibe from this. It's a theory, but here ya go.
I get a feeling the primordial bonfires are the bonfires that spawned where you killed each of the ancient lords in Dark Souls 1. The bright-stone cove are would in that case be the remains of the crystal cave. Perhaps the iron keep was build over the burned remains of Lost Izalith, that would explain the lava at least. The gutter would be Nito's domain, whereas Lost Bastille might have been constructed on the remains of New Londo.
As for the new beings carring what appears like lordsouls, I think it goes with the cycle nature of things.
If I was to give an explaination, I would say the world in Dark Souls follows a repeating cycle. There is a period of Darkness, of timelessness, followed by the apparition of very powerful souls / fire. Fire creates contrasts, it creates time and space, cause without fire, there is only Dark, and dark is basically a void. In a world of darkness and everlasting dragons, there is no time, no contrast, no life or death, just immobility. Those that find the fire, and the lord souls associated with it use it to build empires, to create some sort of civilization, trying to kindle said fire and to keep it from burning out , but there are always forces that want the fire to extinguish, to establish an era of Dark. There are various factions or creatures with different agendas, the ancient dragons, who were once immortal and came from an era before fire, giants, who used to serve alongside the old gods in a past era, but were turned as enemies in recent times, beings from the abyss, that seem to want said abyss to spread and engulf the world. Finally, there's humanity, a strange conundrum. Humans seem to be both beings of light and dark, in the sense where, like fire, they need to consume something to stay lit, devouring souls or humanity fragments to retain the likeness of being normal, but still being cursed with immortality, ever reincarnating, but decaying and becoming hollow beings in the process. Humanity is a curse, because there's no end, no death, only gradual hollowing in time, while the cycle starts anew. Those that have the will to consume souls will last longer, perhaps even acquiring the souls to become a great lord, heck, they might even kindle and link the fires, keeping the age of Dark from swallowing the land, but in the end, the cycle will continue. Time will pass, the fire will slowly fade, traditions and kingdoms will fall. In a sense, I see humanity as fire. It can burn bright, but it can also burn out. Hence the curse, the hollowing, the need to feed yourself to avoid being hollow, the pilgrimage and the idea of kindling the fire.
I think the creation of fire changed the world. Fire created both light and dark after all. My guess is that dragons remember the time before light and dark even existed, where no such contrast existed. It's hard to figure their agenda, since I believe the advent of fire changed the world in a way that cannot be undone : Once there's fire, there's light and dark, and as such, Dragons have to choose between a world of fire or a world of darkness, they cannot go back to their world of timeless and lack of contrast . Some beings are attracted by Dark, beings like Manus, the Primordial Serpents and other beings emanating from the abyss try to bring an age of Dark, trying to mold the world into a place. The Pygmy/Manus/Najandra seem to be a faction of humanity that embraced the dark soul, that hollowing par of the primordial fire. In a sense, they want to see the fire extinguish, to become one with the dark, because to them, the true gift of humanity is the dark soul, that immortal state of being and the power of being part of the abyss.