It seems you've lost the train of your own argument.
> has no context in which it shows such a level of cognitive capacity
You claim LLMs have no context at all in which it shows a similar level of cognitive capacity.
Yet clearly this claim is in contention with the fact that an LLM will indeed be able to evince this, much like a human brain would: by attesting to its own confusion. That is ostensibly empirical and evidential to a nonzero degree.
Thus your claim is too strong and therefore quite simply wrong. Claim mimicry? Then prove human brain consciousness does not derive from the process of mimicry in any form. You can't. In fact, the free energy principle, neuroscience's leading theory of human consciousness, argues the opposite: that prediction and mimicry encompass the entirety of what brains actually do.
https://en.wikipedia.org/wiki/Predictive_coding
> There is no empirical evidence of any awareness whatsoever in any LLM, at all.
And no such claim was made--"awareness" was quoted for a reason.
> It's literally designed to mimic in such a way. And you speak of discussions of consciousness being about the philosophical and unanswerable?
Yes, as this was parent's claim: "They are not cognizant let alone conscious'.
And talking about sloppy argument--it may well turn out that something can be "designed to mimic" yet still be conscious. I'll leave that for you to puzzle out how on earth that might be possible. The exercise might help you form less sloppy arguments in the future.
> You're applying the same notion to something that shows no evidence of awareness while then criticizing assumptions of consciousness in a human brain?
No. But I suppose you've lost the plot a few inferential steps prior this so your confusion is not surprising.
Protip, instead of claiming everything that goes against your sensibilities as nonsense, perhaps entertain the possibility that you might just not be as well informed as you thought.