What is the evidence for specifically allocating "Subhana Rabbiyal 'Azim" (Glory be to my Lord, the Most Great) for bowing (rukūʿ) and "Subhana Rabbiyal A'la wa bihamdihi" (Glory be to my Lord, the Most High, and with His praise) for prostration (sujūd)?

The remembrances (adhkar) mentioned in connection with bowing (rukuʿ) and prostration (sujud) are divided into three types: shared remembrances that are recited in both, such as: "Subhanaka Allahumma Rabbana wa bihamdika Allahumma ighfir li" (Glory be to You, O Allah, our Lord, and with Your praise, O Allah, forgive me), and "Subbuh Quddus Rabb al-Mala'ikati wa ar-Ruh" (Glorified, Most Holy, Lord of the angels and the Spirit), and "Subhana Dhi al-Jabarut wa al-Malakut wa al-Kibriya' wa al-ʿAzamah" (Glory be to the One who possesses Omnipotence, Sovereignty, Grandeur, and Might). And remembrances specific to bowing, such as: "Subhana Rabbī al-ʿAzim" (Glory be to my Lord, the Most Great). And remembrances specific to prostration, such as: "Subhana Rabbī al-Aʿla" (Glory be to my Lord, the Most High). As for adding "wa bihamdihi" (and with His praise) to "Subhana Rabbī al-ʿAzim" or "Subhana Rabbī al-Aʿla," scholars have differed on its authenticity.