Function persist_response 

pub async fn persist_response(
    payload: ResponsePayload,
    ctx: RequestContext,
    conv_handler: ConversationHandler,
    resp_handler: ResponseHandler,
) -> ExecutorResult<()>

Step 3 — Persist the completed response to storage.

Skipped if ResponseStatus is not Completed/Incomplete or payload.id is empty. Routes to ConversationHandler when ctx.conversation_id is set, otherwise ResponseHandler.

Errors

Returns [ExecutorError] if the storage operation fails.