Is the Takbir after every prayer included in the مطلق (unrestricted) Takbir of Eid al-Adha? And is it a Sunnah, مستحب (recommended), or bid'ah (innovation)?

The takbir (proclamation of Allah's greatness) during Eid al-Adha is prescribed from the beginning of Dhul-Hijjah until the end of the thirteenth day thereof. It is divided into two types: absolute takbir and restricted takbir. The absolute takbir begins from the first of Dhul-Hijjah until the eighth day. The restricted takbir occurs after the obligatory prayers. The combination of both absolute and restricted takbir takes place on the Day of Arafah, the Day of Sacrifice (Eid al-Adha), and the three days of Tashreeq. A pilgrim performs the talbiyah (chanting of 'Labbaik Allahumma Labbaik') until throwing the pebbles at Jamarat al-Aqabah, then he performs the takbir. It is recommended to perform the takbir from the very first pebble thrown.