Al-Daraqutni and al-Bayhaqi narrated it. This ʿUzrah is deemed acceptable by al-Hafiz Ibn Hajar when corroborated, and, as you have seen, a number of narrators did corroborate him.
It was also corroborated by Yahya ibn Abi Kathir, from Abu Salamah, who said: Abu Hurayrah narrated to me, in a report attributed to the Prophet, peace and blessings be upon him: “Whoever performs one rakʿah of the Dawn prayer before the sun rises has not missed it; and whoever performs one rakʿah of the Afternoon prayer before the sun sets has not missed it.” Ahmad narrated it (2/254), and its chain of transmission is authentic according to the criteria of both al-Bukhari and Muslim. Al-Bukhari also narrated it in similar wording; its wording has already preceded under no. 66. Some narrators added the word “first” in connection with each of the two prayers, so refer to it there. Ibn Hibban also authenticated it (1584).
Al-Kawthari likewise sought to declare this defective on account of Yahya ibn Abi Kathir’s ambiguous use of “from,” disregarding the fact that both al-Bukhari and Muslim relied upon him without qualification, and that al-Bukhari relied upon this particular hadith of his. Even if that were a materially weakening defect in this chain, it would not undermine the hadith’s authenticity, since it has come through those many authentic routes, as is well known to those versed in this noble discipline.
It has other routes as well. Al-Tayalisi said in his Musnad (2381): Zuhayr ibn Muhammad narrated to us, from Zayd ibn Aslam, from al-Aʿraj, Busr ibn Saʿid, and Abu Salih, from Abu Hurayrah, with the same wording as the hadith of Ibn Abi Kathir. This is a sound chain of transmission; its narrators are those of al-Bukhari and Muslim. Ibn Hibban authenticated it as well (1581).
After gathering all the routes of this hadith, it becomes clear to anyone with eyes that it explicitly proves the invalidity of the Hanafi position, which holds that if the sun rises while someone is performing the Dawn prayer, his prayer is invalidated, even if he has completed one rakʿah of it! They have been highly inventive in evading these hadiths: at times, by declaring whichever of them they can to be defective, even on the basis of a non-substantive defect; at times, by disregarding the authentic routes, as the partisan of the present age, Shaykh al-Kawthari, has done; at times, by claiming that they were abrogated by the hadiths prohibiting prayer at sunrise; and at times, by restricting them to children and the like, as al-Tahawi did, followed by al-Kawthari.