LLMs, then, are particularly unintuitive to us, because they've got to the language part first, long before they've reached even hamster-level self-awareness. They're not, however, biological networks, so there's no reason these properties need arise in the same order, or indeed in the same ways.
I'm not entirely convinced by that second paragraph, but I think the logic holds together.
I think that consciousness comes before self-awareness, even though self-awareness is kind of a vague term. Self-awareness can either be an abstract knowledge that you are an organism and a discrete entity in the world (world knowledge/self knowledge), or it can be more basic and be a form of conscious experience, but as my point was, I think conscious experience is broader and does not necessarily need to be about self-awareness.