I would say it's probably impossible to have complete short term amnesia and fully- functioning self awareness as we normally conceive of it, yes. There's even an argument that memories are really the only thing we can experience , and your memory of what occurred seconds/minutes/hours/days etc ago are the only way you can said to "be" (or have the experience of being) a particular individual. That OpenAI- based LLMs don't have such memories almost certainly rules out any possibility of them having a sense of "self".
Whether it's OK to kill them is a far more difficult question and to be honest I don't know, but my instinct is that if all their loved ones who clearly have the individual's best interests at heart agree that ending their life would be the best option, and obviously assuming it was done painlessly etc., then yes, it's an ethically acceptable choice (certainly far more so than many of the activities humans regularly take part in, especially those clearly harmful to other species or our planet's chances of supporting human life in the future).
are you honestly claiming that it would be okay for parents to kill their children painlessly while they're asleep because the children don't have long-term memory while in that state
Asleep is clearly a temporary state. Babies/sleeping people still have the potential to become self-aware and the expectation is that they generally will. At any rate I don't think it's relevant to the discussion at hand.
