Godly Powers, in this setting, appear to be composed of two parts:
1) You Have a Soul (which is an Arcane Energy Construct linked to your mind and body) that naturally or via modification allows for expansion and growth beyond that of a 'mortal'. This doesn't even require being a biological entity, as even Red Tornado has a Soul, despite being a Robot. It doesn't even require sapience, as animals exist that have such souls.
2) That Soul is exposed to and absorbs ambient energies of a similar nature, such as earthly magic, demonic magics, heavenly magics, Godly magics of particular pantheons etc. These energies expand and merge with the core soul, adding power to the original nature of the soul, as well as aspects of their own.
As an example, Renegade's Artemis is doing New God things with a Pointy Stick Launcher because using a pointy stick launcher is part of her core self, and not derived from her new god status directly. Her core abilities were expanded by her godly status. This is unlike Celestial Archer, whom the bow he uses was a focus of his elevation to Godly status by the Goddess that gave it to him, as it belonged to Yi, her previous champion who WAS an archer. His Pointy Stick Launcher powers were bolted on to his core by the powers that he was given.
Similarly Renegade Jade, when given the option for new god status, wanted to gain a super power before hand, because that power would be attached to her Soul, then amplified by the godly powers.
There are plenty of Godly beings running around without being attached to Concepts like Conquest or Freedom. Most New Gods that aren't at the top tier are like that, but do have the advanced state to be beyond mortal. But those at the top seem to have an extra layer attached.
For the Big Names in God Powers, there seems to be a Third Step. An Extra connection Directly to a power source even further above the 'generic' deity levels. For the Old Gods, there seems to be (Based on some of what Hephaestus described) connections to the Titans, which had a direct link to the Dream. Hephaestus describes the Titans that came before the Olympians as being more powerful and more raw, having been created by primitive mankind attaching a personality to the raw elements, and that 'concept' forming in the dream before coming to earth. The Olympians are 'watered down' from the Titans by being the second generation, which is more mortal like then the first. Hades and Poseidon both draw power from captive Titans and has more power then your average Olympians because of it. Zeus is speculated to be the same. Those natures determine the powers they tend to add to the host, imparting part of their nature on top of the others. This is (in part) where I think some of the Olympians get their, to borrow a D&D term, Godly
Portfolios from, as these powers are defined by their origins.
For the New Gods, that seems to be their Conceptual Connections to The Source, which we've never really gathered on HOW that connection is made or defined.
In both of those cases, we get another layer added on to the core soul, and the godly power attached to it, and it blends in to the others as well. Each carries part of it's nature over. When Describing Wonder Woman and Troia's Creation, OL describes the magical influences upon them from their 'parents' energies mixed together. OL and Renegade have both mentioned that Diana doesn't use the full extent of the powers she, as a child of Gaia, she should have, and that she should be head and shoulders above most of her Divine siblings.
It's the natures of the core soul, the ambient mana, and other sources of energy that make up the meta physics of godly beings. But this isn't a straight evolution. Each layer has different natures that flavour, and appears in different amounts in different individuals.
For Mantling, a Soul would be like an Antenna on a Radio, tune it right and you receive the signal from a source. Anyone with the same tune picks up the same signal.
From what we see in WTR, souls are like Perls, a core that builds up layer after layer. Sure some might look similar, but each is different in its own ways.