I'd argue that's "underlying hidden authorial style" as opposed to what most people mean when they refer to the "personality" of the thing they were "chatting with."

Consider the implementation: There's document with "User: Open the pod bay doors, HAL" followed by an incomplete "HAL-9000: ", and the LLM is spun up to suggest what would "fit" to round out the document. Non-LLM code parses out HAL-9000's line and "performs" it at you across an internet connection.

Whatever answer you get, that "personality" is mostly from how the document(s) described HAL-9000 and similar characters, as opposed to a self-insert by the ego-less name-less algorithm that makes documents longer.

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