I said: He did not clarify whether any of this is actually reported, nor whether it is firmly established. Therefore I say:

As for the phrase of glorification, it is sound and firmly established from Ibn ʿAbbās and others, and is recorded in Sahih Abū Dāwūd 826.

What precedes it, however, comes through a hadith of Abū Hurayrah, traced back to the Prophet ﷺ with the wording:
“Whoever among you recites, ‘By the fig and the olive…,’ and when he reaches its ending—‘Is not Allah the best of judges?’—let him say, ‘Indeed…,’” and so on.
Abū Dāwūd and others transmitted it, but its chain contains an unnamed man whose status is discussed in Daʿīf Abī Dāwūd 156 and al-Mishkāt 860.

What is authentically established from that report is only his saying “Indeed” (balā) after the verse in Sūrat al-Qiyāmah. Mūsā ibn Abī ʿĀʾishah narrated:
“A man used to pray on the roof of his house, and whenever he recited, ‘Is not that [Lord] able to give life to the dead?’ he would say, ‘Glory be to You—indeed!’
When they asked him about it, he said, ‘I heard it from the Messenger of Allah ﷺ.’”
Abū Dāwūd narrated this with an authentic chain from that man, who is a Companion; his unknown identity does not harm the report, as the scholars have explained. For this reason I included it in Sahih Abī Dāwūd, no. 827.

His statement while listing the recommended acts of the prayer: “7. The takbīrs of the prayer.”

I say: To count these takbīrs among the sunnahs contradicts the Prophet’s ﷺ order to the man who prayed incorrectly to pronounce them, as appears in a narration of Abū Dāwūd and others from Rifāʿah ibn Rāfiʿ—recorded in Sahih Abū Dāwūd 803–805. They are therefore obligatory, further supported by the general instruction of the Prophet ﷺ: “Pray as you have seen me pray.”