Bukhari

Hadith Commentary:
➊
It appears that Imam Bukhari rahimahullah inclines to the view that on the occasion of the conquest of Makkah, the Messenger of Allah sallallahu alayhi wa sallam entered Makkah from the upper side, and Hafiz Ibn Hajar rahimahullah has also supported this position, because he has explicitly stated that at the time of the conquest of Makkah, the Messenger of Allah sallallahu alayhi wa sallam entered from the upper side (Fath al-Bari: 8/23. ).
Although, in a previous narration, it is clarified that the Messenger of Allah sallallahu alayhi wa sallam had ordered Khalid ibn al-Walid radi Allahu anhu to enter from the upper side, while he himself entered Makkah from the lower side.
(Sahih al-Bukhari, al-Maghazi, Hadith: 4280. )

➋
Our inclination is that on the occasion of the conquest of Makkah, he entered first from the upper side and then from the lower side.
And Allah knows best.

Hadith Commentary:
(1)
There are three locations in Makkah Mukarramah with nearly identical names, the details of which are as follows:
٭ KADĀ’:
This is the mountain pass that descends towards Jannat al-Mu‘alla, which is the famous cemetery of the people of Makkah.
Nowadays, it is called Hajūn.
٭ KUDĀ:
This mountain pass is towards the mountain of Qaiqan, near Sha‘b Shāmiyyīn, by the gate of Shubaykah.
٭ KUDAY:
This is the location that is the route from Makkah towards Yemen.
From this direction, the people of Yemen used to enter Makkah.

(2)
From these ahadith, it is understood that entering Makkah Mukarramah from the direction of Thaniyyah ‘Ulyā and exiting from the direction of Thaniyyah Suflā is recommended (mustahabb).
In this recommendation, those performing Hajj or ‘Umrah and those entering without ihram are all equal.
It should be noted that when ‘Urwah (rahimahullah) narrated the hadith, he mentioned the action of the Messenger of Allah (sallallahu alayhi wa sallam), indicating that entering Makkah Mukarramah from the upper side is not obligatory; therefore, ‘Urwah (rahimahullah), for the sake of ease and convenience, used to come to Makkah from the direction of Kadā’, because for him, this route was closer to reach Makkah from his home.

(3)
Imam Bukhari (rahimahullah), after narrating the ahadith, clarified at the end that Kadā’ and Kuda are the names of two different locations.
Hafiz Ibn Hajar (rahimahullah) writes that such an explanation was not particularly necessary, because from the context of the hadith itself, it is evident that these are two separate locations in the outskirts of Makkah.
(Fath al-Bari: 3/553)
Perhaps Imam Bukhari (rahimahullah) considered it necessary to clarify this due to the similarity of the words.
And Allah knows best.

(4)
Hisham ibn ‘Urwah has narrated this hadith both as mursal and as musnad (connected).
Imam Bukhari (rahimahullah) mentioned both chains of transmission so that no deficiency is implied in the musnad narration due to the mursal narration, because the musnad narration has been narrated by Sufyan ibn ‘Uyaynah, and in the mursal narration, two trustworthy narrators, ‘Amr and Hatim, have supported and corroborated it.
As a form of corroboration (mutaba‘ah), mursal narrations can be presented.
And Allah knows best.