What is the religious ruling on the tashriq takbirs, and who recites them and when?

There are narrations that the Prophet (peace and blessings be upon him) recited the tashriq takbirs after the obligatory prayers, starting from the morning (fajr) prayer on the day of Arafah until the afternoon (asr) prayer on the fourth day of Eid al-Adha, including the asr prayer (Beyhakî, es-Sünenü’l-kübrâ, 3/438-440 [6273-6278]; Dârekutnî, es-Sünen, 2/390-391 [1735-1737]).

Accordingly, in the preferred view of the Hanafi school, it is obligatory (wajib) for every Muslim, male and female, to recite the tashriq takbir after each obligatory prayer for 23 prayer times, from the morning prayer on the day of Arafah until the asr prayer on the fourth day of Eid. If a prayer is made up (qada) during the tashriq days, the tashriq takbir is also recited after it. However, if the missed prayers are made up after the tashriq days have ended, the takbir is not recited. The takbirs are not made up unless the prayer itself is made up (Serahsî, el-Mebsût, 2/43-44; Ibn al-Humam, Fath al-Qadir, 2/80-82).

According to the Shafi'i school, the tashriq takbirs are considered sunnah (recommended) (Mâwardî, al-Hâwî, 1/484).

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu