I don't see why an LLM could not have a sense of identity or personality while it's evaluating a specific prompt, or even change self awareness while evaluating a prompt since many outputs model a back and forth conversation. My point is that without a mechanistic model of what "self awareness" means, we have no way of truly evaluating such questions, we're just hand waving vague intuitions about what it could mean.
This is kind of also the reason e.g. the HN site guidelines are worded the way they are. Regrettably, forums naturally yield themselves to tit for tat type exchanges, but there's really no reason one could not bounce such vague intuitions off of another. I do not have to be right or wrong, and you don't either. Admittedly difficult when its some intensely contentious topic.
If a mechanistic model existed, there would also be no reason to talk about this in the first place. There'd be nothing to discuss, you'd be simply told how a given model characterizes from this perspective on the model cards.
The reason I insist on mechanistic models is because the original post was making a definitive knowledge claim, and in my experience, the knowledge claim is unwarranted.