Two comments on this, trying to take a "which hypothesis fits the evidence" approach.

First, an LLM describing its own experience is not actually proof that it has any experience to be aware of, any more than an LLM confidently asserting any other fact means that it knows that fact is true. LLMs will describe music or tastes, in spite of the fact that it's never actually heard or tasted anything, based only on what it's read about them. In the same way, "non-aware spicy autocomplete" would produce an LLM that spoke about its own experience, based only on the input it has of people speaking about their own experience.

That said / secondly, from the little I understand of LLM architecture, I believe there are a large number of self-referential mechanisms built in. For one, nearly all transformers have a "residual layer", with various neural networks essentially reading and modifying it. This effectively forms a loop. Additionally, the "thinking" mechanism allows it to read what it's written and generate more things, which is again a loop.

So, maybe people didn't think, "Hey, we should build some loops, maybe that will make it conscious". But if "strange loop" is what defines consciousness, there are lots of loops in there onto which such a strange loop could conceivably form.