In late antiquity Hekate was an important Goddess in the Chaldean Oracles and the Theurgy of neoplatonism.
The Chaldean Oracles are oracular texts that were channelled through trance-mediums. The Gods were invoked into young boys. The gods spoke through these boys to the people who invoked them. And the oracles were written down. Most surviving fragments of these oracular texts survived for us through the writings of neoplatonists who wrote comments about them. Or through church people who quoted the oracles in their texts against the pagan cults.
The Chaldean Oracles got their name from Julian the Chaldean- he lived in Rome (the city) while he wrote down the oracles. And his son continued the work of his father- Julian the Theurg. So the oracles are not named after ancient Chaldea (the land) but after the composer (Julian the Chaldean).
Most fragments of the oracles were spoken by Apollon-Helios and Hekate.
In the fragments of the Chaldean Oracles and in the interpretation of those through the neoplatonic philosophers and practitioners of their theurgy we know that Hekate was a kind of Great-Goddess in this context.
In this worldview there are three worlds- the material world (our world- which contains the sphere of planets above us and the Tartaros below us). The etheric world– which is the world of soul, daimons and spirits (like our modern view of the astral world). And the empyrean world (divine world). The etheric world mediates and connects the material world with the empyrean world (and separates the two at the same time).
The main Gods:
There are three great Gods in this worldview. Had (the first father, first fire- supreme first being), Hekate and Hadad (the second father, second fire). Had is the pure divine and has his realm outside of the cosmos. Hekate emanates out of Had and is a hypostasis of him. Hekate bore the second father (Hadad) and from her womb the worlds were born too (and the angels, the world soul, nature and her three virtues: Love, faith and truth).
I will now try to explain the view of Hekate in this system or worldview. This is filtered through my own understanding of this (sometimes quite complicated) topic. So all what follows is my personal interpretation- but influenced by personal experience of the Goddess, too.
Had has just one emanation- he exists just in the highest and purest sphere of the empyrean world. Hadad has two emanations- he exists in the empyrean world and in the material world at the same time- divine spirit weaved into matter.
Hekate has three emanations- she exists at the same time in the empyrean world, etheric world and the material world (and these worlds were born from her womb). She is outside of the three cosmic worlds (on the threshold to Had) and within the cosmos (in all three worlds). Through this she is one Goddess in her hypersocmic form- but threefold in her cosmic form. Together the Gods build a harmony.
She has different roles in these worlds or manifests herself different in each of the three worlds.
The empyrean Hekate:
In the empyrean world Hekate has her sphere below the sphere of Had.
She has her place on the threshold between the supreme and pure divinity- and the lower empyrean spheres. She mediates between the first father Had and the second father Hadad. She is in the centre of all things. At the same time hypercosmic (like Had) and cosmic (Hadad). So she is at the same time hypercosmic (outside of the cosmos) and cosmic (in the cosmos)
In the empyrean world she is the mother or source of angels (messengers who mediate like herself), the source of the three great virtues (love, faith and truth). And she is great Soteira- the saviour.
Through the great empyrean Hekate the practitioners of Theurgy were able move out of the circle of rebirth and do go back into the sphere of Had. Hekate Soteira was able to guide the spirited souls of the theurgs back into the haven of Had (and so free the soul/spirit from new incarnations). In the empyrean spheres Hekate has strong solar attributes.. She is a Great Goddess- the three worlds were borne from her womb, the light, the aether, the world soul, fate and nature.
The etheric Hekate:
In the etheric sphere Hekate is the ensouler of the cosmos- and was equated with the world soul of Plato. She mediates between the Gods of the lower empyrean spheres and the material world (similar to her mediating role between Had and Hadad in the empyrean world). She is the ruler of daimons (who do the same job like she herself- they connect the Gods through the etheric world with the material world- or the worshippers with the Gods through the interaction of the daimons).
She is connected to the moon- who also mediates between the worlds. And the moon was envisioned as the abode of the realms of Hades (where the dead found their resting place) and the Elysian Fields (were special humans found their resting place or the people who were initiated into the mysteries).
So in the lunar sphere she can act as Soteria (saviour) too, through her influence souls can find abode in the Elysium instead of the Hades.
The material Hekate:
In the material world Hekate appears more like she was viewed in the traditional religions of the greco-roman world. She is the ruler of earth, sea and sky (as physical places). She is Physis (nature) and fate. Where the etheric Hekate had the power to connect the soul of the theurgists with their spirits and draw them up to the empyrean spheres- the material Hekate draws the souls down from the etheric world into embodiment- into physical incarnation. Because of that they tried to avoid the influence of the material world and of material Hekate.
I personal don’t see the material Hekate as negative (like the neoplatonists interpreted her) but this aspect is for me personal quite important. For me she is nature and I can find the divine weaved into nature. In the oracles nature was described as the living mantle of Hekate.
In this worldview the Tartaros (as the place of punishment for the souls of “evil” people) is not located in the etheric sphere of the moon (like the Hades or the Elysium) but is located in the lowest manifestation of the material world. It is within the earth and ruled by Hekate-Echidna as mistress of the Tartaros.
Hekate is described in her material forms quite similar like she is depicted in the PGM. There she is a Great-Goddess, but quite material. She is change, fate, growth and death, beginning and end. And I think this is the key to understand the material Hekate. She is more ambivalent than in her etheric- or empyrean forms.
So in the worldview of the Chaldean Oracles Hekate is not just the world soul- but she has emanations in all three worlds. She is material, etheric and empyrean. For me she is like a kind of world-tree in this system. She is the source of the worlds- but at the same time an embodiment of each world. She is cosmic and hypercosmic.
Like a world tree she connects the worlds with each other- she is on the lowest point (Tartaros in the material world) and on the highest point (on the threshold of the sphere of Had) at the same time. And she is on all the thresholds of the different worlds. Guarding the portals- mediating and separating at the same time.
Good sources about Hekates roles in the Chaldean Oracles are these books:
Hecate by Stephen Ronan
Hekate die dunkle Göttin by Thomas Lautwein.
And Hekate Soteira by Sarah Iles Johnston (but she focuses more on her role as world-soul).