The four fundamental states of matter are solids, liquids, gasses and plasma. It's not a precise or scientific comparison, but still a comparison given how there is four of them and how the states of matter relate to the common elements that are bended.
That's the thing, they don't relate. Fire is generally not a plasma, & saying that it's similar because there are ions doesn't make sense because liquids & solids have ions all the time. Plasma is specifically the point at which electromagnetic interactions begin to dominate the way the structure acts. Further, most of the water universally is ice, & even if you want to limit to the earth, only a small portion of the that is solid rock as we know it.
If the comparison isn't accurate, then it's not a very good comparison. And the fact that it's not scientific is relevant because (aside from the fact that this topic explicitly asks about physics) you said the exact words "the ancient scholars were still pretty accurate to modern sciences on states of matter" & still seem to think that.
Ancient scholars who theorized the four classical elements perhaps used the elements themselves for metaphors of the states of matter that they understood at the time.
Case in point, this is not what happened. Unlike fire, earth, water, & air, there is no ancient word referring to what we know as plasma. The only plasmas anyone knew about were lightning & in some cases auroras, both of which ancient people thought were spirits or magic from the gods.
But not only did they not know there was a 4th state, it doesn't seem like ancient people even had a concept of states of matter, at least not that I can find mention of. Of course they knew that water could freeze & metal could melt, which might be one reason why they thought water is an element, but people didn't think their Classical Elements were different forms that a piece of matter could cycle through, they thought of them as the way we think of the Periodic Table.
If you don't know what those people actually believed, you can try looking it up, but you shouldn't just guess. Especially because the notion that ancient people believed basically the same things we do now is a type of cultural bias. In some ways they may have, but in other ways they believed in shit like the 4 humors, while certain concepts we take for granted would be totally alien to them.
But also some other cultures also had other additional elements such as wood, metal or as you mentioned aether.
Which are equally unscientific.
superheating gasses can ionize them into plasma.
I know I said it didn't matter earlier, but when you say "further heated" & then also "superheated" when describing the same thing, it really sticks out.
Roku (plasma) became Aang and Aang (gas) became Korra and Korra (liquid) will be born an earthbender (solid) in her next life.
Further freezing a solid doesn't create a plasma, so it goes back to the point that there being 4 classical elements & 4 basic states of matter is an amusing coincidence that doesn't really coincide that much.