Imam al-Shawkani affirmed in Nayl al-Awtar 2 / 222–224, and again in al-Sayl al-Jarrar, that the default ruling for every matter mentioned in the ḥadith of the man who prayed incorrectly is that it is obligatory. He even stated explicitly in Nayl that these takbīrs are among the matters cited in some versions of the report, but he then forgot this in al-Sayl and, in 1 / 227–228, listed them among the recommended practices. Glory be to my Lord, Who neither errs nor forgets.
Imam Aḥmad—may Allah have mercy on him—also held them to be obligatory, as al-Nawawī records in al-Majmūʿ 3 / 397, citing the general proof mentioned earlier on his behalf. The ḥadith of the man who prayed badly, however, escaped al-Nawawī’s attention, for he argued against Aḥmad, saying: “Our evidence against Aḥmad is the ḥadith of the one who prayed poorly, since the Prophet ﷺ did not command him to pronounce the transitional takbīrs; he only commanded him to utter the opening takbīr!” Thus he failed to notice the narration of Abū Dāwūd and others.