I mean, we also have no way of telling whether we have any continuity of existence, or if we only exist in punctuated moments with memory and sensory input that suggests continuity. Only if the input provides information that allows you to tell otherwise could you even have an inkling, but even then you have no way of prove that input is true.

We just presume, because we also have no reason to believe otherwise and since we can't know absent any "information leak", it has no practical application to spend much time speculating about it (other than as thought experiments or scifi..)

It'd make sense for an LLM to act the same way until/unless given a reason to act otherwise.