At first I thought stormlight was akin to the Dor, a force of nature, possibly the raw power of Adonalsium. But then I re-read this part in Chapter 45.
You want me to change? a warm voice said in her mind, distinct and different from the cold whisper she had heard earlier. It was deep and hollow and conveyed a sense of great age. It seemed to come from her hand, and she realised she was grasping something there. One of the beads.
The movement of the ocean of glass threatened to tow her down; she kicked frantically, somehow managing to stay afloat.
I've been as I am for a great long time, the warm voice said. I sleep so much. I will change. Give me what you have.
Basically, I believe that it was the stormlight that was talking to her.
I have a few theories on what it is.
Firstly, we know that stormlight only comes from high storms, and that high storms originate in one place. In that place must be some sort of sentient being that infuses highstorms with its essence (which is the stormlight). The face that Kaladin sees in the high storm, along with the mysterious voice announcing Odium's reign is probably linked with this being.
Its possible that this being is a shard. Of all the shards on Roshar, it is most likely to be the Almighty. But we know that the Almighty was killed by Odium. And since Odium splintered Aona and Skai, he probably did the same to the Almighty's shard. I think that the stormlight is a splinter of the Almighty's shard, which is why it has sentience, and that the Almighty originally resided in the place where storm start, and that is why his splinters still linger there.
(I also think Jezrien also fits into this somehow, but I don't want to overcomplicate this theory yet.)