Short answer, no, there is no retrieving from OpenAI API safety and logging system. The unique ID of a completion has no direct use to you.
OpenAI has a newer autonomous agent called “assistants” available on API, which maintains a conversation session for you, which much be run against a specially programmed AI backend method. It is somewhat limited, as the purpose is just to expose a mechanism for placing a user message “in”, and waiting for an assistant response “out” (and then unlimited conversation is still passed to the model every new input and run, growing up to the AI’s limits.)