Inrau had found his grotto in the shrine of Onkis, the Singer-in-the-Dark, the Aspect who stood at the heart of all men, moving them to forever grasp far more than they could hold.
Some were grotesque, like the severed head of Onkis upon a golden tree [...]
The idol was worked in white marble, eyes closed with the sunken look of the dead. At first glance she appeared to be the severed head of a woman, beautiful yet vaguely common, mounted on a pole. Anything more than a glance, however, revealed the pole to be a miniature tree, like those cultivated by the ancient Norsirai, only worked in bronze. Branches poked through her parted lips and swept across her face—nature reborn through human lips. Other branches reached behind to break through her frozen hair. Her image never failed to stir something within him, and this is why he always returned to her: she was this stirring, the dark place where the flurries of his thought arose. She came before him.
Her symbol is the Copper Tree (which also happens to be the device of the legendary Nonman Mansion of Siol, though no link has been established).
From Duskweaver here, sometime in the distant past:
Specifically the mansion of Siöl. Onkis' version has the tree growing through a woman's head, though. Which inclines me to wonder if perhaps it's a reference to Cû’jara-Cinmoi's forgiveness of Nin'janjin, a mercy which led directly to the womb-plague which claimed as its first victim Cû’jara-Cinmoi's own wife. It'd be funny if the symbol of the goddess of compassion was actually a warning about the dangers of extending compassion to those who don't merit it...
Onkis is also described as "a prophetess, not of the future, but of the motivations of Men", which makes her sound a bit like a Dûnyain. Arguably, of course, that's what 'compassion' really means: understanding the movement of others' souls. It does not necessarily have to imply 'being nice'.
I think what links them are the concept of ambition (IIRC, Onkis is said to tempt men to always try to grasp more than they can hold - as Cu'jara Cinmoi did in conquering Viri) and the way in which our present choices are constrained by history (i.e. they seem to spread out freely like the branches of a tree, but are in fact held within strict bounds by where the tree first rooted - by what has come before us).
So, I really don't believe that the pointing out of the similarity between Onkis' symbol and the Copper Tree of Siöl is a coincidence. The fact is that we are purposely left with little information as to what happened to Siöl after the Apocalypse. We know what became of Ishterebinth, and Cil-Aujas, yet Siöl was regarded as the great mansion and we don't even know where it is. We are offered only clues, of which I believe one of is the Copper Tree connection.
Two alternative possibilites:
Considering that Onkis was perhaps created by the fall of Siöl, or the process there-within, by the Nonmen themselves, attempting to worship their dead wives, perhaps in the hope that some redemption could be found in piety for their earlier over-reachto attain immortality. There is anecdotal evidence that immortality wrecked the old Oblivion-worship for the Nonmen, perhaps because the rewriting of the Tusk damned them a priori.
Perhaps even created the Norsirai that probably destroyed the mansion, or at least took over the area that once comprised Siöl stumbled upon a topoi (perhaps a mass grave of the Siöli women?). Consider the image, a statue of a copper tree, over witch a wright, like the one in Cil-Aujas, appears to them, looking as a head with a tree grown through it. Pretty sure that would make a good impression on early Men, perhaps inspiring what would become worshiped as Onkis.
Just some ideas that randomly came to me.