Is the takbir made by one who joins the prayer late, upon standing to complete his prayer after the Imam has given the salutation, considered an extra takbir given that he has already made the takbirat al-ihram?

This takbir is not extra; rather, it is the takbir for standing up for the first rak'ah of the prayer. Takbir when lowering and rising during prayer is legislated by the consensus of the jurists. The worshipper should say the takbir from the beginning of standing. Indeed, Ibn Az-Zubayr used to say the takbir when rising, and Abu Sa'id al-Khudri vocalized the takbir when he raised his head from prostration, and when he prostrated, and when he rose, and when he stood up from the two rak'ahs, and he said: "This is how I saw the Prophet, peace and blessings be upon him." The word "when" indicates that the takbir accompanies the action in all transitions, and this is the most sound opinion and the view of the majority.