Arguably LLMs are showing that self awareness or self reference is a property that comes "for free" or as a corollary of more generic requirements. It used to be that self/consciousness would be a very mysterious and difficult thing to achieve but the point is that in practice they didn't even have to try, it just came as a byproduct of learning from the input data (corpus of human examples), and also the ability to talk about arbitrary things and thus itself.