What does it mean to be aware that you are aware of something, beyond being aware of that thing?

This devolves upon of the mechanism of awareness. Animals have models of the world. A model is an internal state that is related somehow to an external state. Such models have evolved for their utility—they supplant the sense organs to a degree. Sometimes the model can be consulted in lieu of the world via the senses.

Perhaps we should distinguish between the model whose purpose is to avoid sensing again, or to remember how things were, as alternatively a signal which is part of stimulus response reflex.

When applied to humans, a ‘world model’ typically includes cultural elements. Perhaps most people include local religious elements in their weltanschauung which is the same as world model.