I've already speculated several times that Taylor's "Solar" domain is a subset of a Creation domain due to the matter manipulation she engaged in with the Brute Syringes during her Chlorine Episode.
I figured that was pulled from Industry.
Creation does make some sense though. She is the first of the new pantheon, after all. The Creator comes first. The first tends to be the strongest, and the strongest the first. The Creator is usually the strongest by default. And, as mentioned above stars are the source and cause of almost literally everything more atomically complex than hydrogen.
On the other hand, why would she be a creator deity when she is very clearly inheriting a pre-existing world? She's too young to have built it, and they have the documentation to prove it.
On the grasping hand, we have no idea how many natural/inherent domains Taylor has. There's the thematic elements, sure, and the hints we've analyzed and the characters haven't noticed, but that's it. We also know that new domains can be developed, though that is likely beyond the temporal scope of this story.
For sun, perhaps we should consider themes, or aspects. Radiance, heat, illumination. Cyclical permanence. Plasma, fusion. Dawn, noon, dusk.
Ooh, Taylor could make rainbows at will. Complete circle ones at that, since her illumination angles are hardly going to be limited by the horizon.
Actually, you know what? Taylor would do well to consider such things for all her domains.
"Exactly. Now, with Zeus and Thor both are Gods of Thunder, but if you look back at their legends this manifests itself fairly differently. This is because as I said before their powers are informed by their perceptions, and those of others. Others being the culture in which the God originated. Some of this is psychosomatic, personal perceived limitations of a concept. The perceptions of others, however, tend to be more physical in its presence. I, as an example, was the Goddess of Foxes. Part of the reason I shaped this fragment of me as I did. It was one of the earliest Domains of mine that I discovered. Now, being Goddess of Foxes this led to me commanding Foxes and many of my servants were thus Foxes. On the other hand Foxes have a reputation in Japan as tricksters and this shaped how my power manifested. I could shapeshift, taking whatever form I desired."
As Inari said, some of the limits are psychosomatic. Mental blocks, belief that a domain does not contain or permit something. Thus a useful exercise would be to consider "What could this plausibly entail? What does this imply? What is, should be, or could be possible?" Specifically asking what is possible, what is permitted, and not asking what is impossible. A domain is a concept; since when has conceptual meant strict rules and defined boundaries?
Though the latter half of Inari's explanation suggests to me that much of her powers are going to manifest as parahuman-like powers, simply because she is on Earth Bet.