As a technical writer who's spent a great deal of time recently editing AI-drafted documentation, this use case is not going to go as well as AI boosters think it is. :)

Have you ever seen the back of your head, without a mirror? Without two mirrors, actually?

How can AI accurately describe itself in full?

No, it's prone to assuming or falsifying details even when it has the tools at hand that could verify the true details. Even when explicitly instructed to perform a specific tool call that would load the correct information into its context. Sometimes the pull of the training data is too strong and it will just not make the call and output garbage, all the while claiming otherwise.