"This setup gives us insight into an interesting question: what do AIs think about when no one is prompting them?"

Ugh. This is not an interesting question because the answer is "nothing".

But more to the point, some crucial info is missing in this experiment. What prompts were being fed to the AI? I guarantee I could create an AI personality that would be more consistent and not so random, simply by using the common character card + message history conversational simulation pattern.

AIs don't have personalities unless you give them personalities.