Bukhari

Hadith Commentary:
In this hadith, Hazrat Aisha Siddiqa (radi Allahu anha) has also referred to the Sunnah prayers of Fajr with the word "nafl" (supererogatory prayer).
Thus, there is concordance between the chapter heading and the hadith.
It is also understood from this that the Messenger of Allah (sallallahu alayhi wa sallam) maintained regularity (mudaawamah) in performing these Sunnah prayers.
Therefore, whether in travel or at home, it is not preferable to abandon them anywhere.

Hadith Commentary:
(1)
In the hadith, the two Sunnah (regular voluntary) units before Fajr are described as supererogatory (nawafil), but the Messenger of Allah (sallallahu alayhi wa sallam) was extremely diligent in performing them, to the extent that he did not abandon them even during travel.
Some scholars have referred to them as "tatawwu‘" (voluntary prayer), as when Abdullah bin Shaqiq asked Aisha (radi Allahu anha) about the voluntary (nafl) prayers of the Messenger of Allah (sallallahu alayhi wa sallam), she included the two Sunnah units of Fajr in her response. Likewise, Ibn Jurayj asked Ata whether the two Sunnah units before Fajr are obligatory or if they are considered voluntary prayer (tatawwu‘), so he narrated the aforementioned hadith, meaning that despite being voluntary, the Messenger of Allah (sallallahu alayhi wa sallam) was consistent in performing them and was diligent in their observance.
(Fath al-Bari: 3/58) (2)
Due to the Messenger of Allah’s (sallallahu alayhi wa sallam) strict adherence to them, Imam Hasan al-Basri (rahimahullah) declared them obligatory, as is explicitly stated in Musannaf Ibn Abi Shaybah.
There is also a narration from Imam Abu Hanifah (rahimahullah) regarding their being obligatory.
Hasan bin Ziyad narrated from him that if someone performs them sitting without excuse, it is not permissible.
(Fath al-Bari: 3/56)
In any case, there is great emphasis in the hadiths on performing the two Sunnah units before Fajr.

Hadith Commentary: Benefits and Issues: To hasten in performing the Sunnah prayers of Fajr is an indication of their importance and preservation, and it points to the fact that the Prophet (sallallahu alayhi wa sallam) was consistent in ensuring that they were performed before the obligatory Fajr prayer. There was no need to make up these Sunnah prayers after the Fajr prayer. However, nowadays, we do not give these Sunnah prayers the same level of importance, which is why many people perform them after the Fajr prayer, even though that is not their actual prescribed time.

1254. Commentary:
The Messenger of Allah (sallallahu alayhi wa sallam) would not abandon the Sunnah prayers of Fajr even during travel; for this reason, some hadith scholars, such as Hasan al-Basri (rahimahullah), have considered them obligatory (wajib), as has Imam Abu Hanifah (rahimahullah). From this, it becomes clear that, in comparison to other Sunnah prayers, these two Sunnah units of Fajr hold much greater significance.

Takhrij:
«أخرجه البخاري، التهجد، باب تعاهد ركعتي الفجر، حديث:1169، ومسلم، صلاة المسافرين، باب استحباب ركعتي سنة الفجر، حديث:724، وحديث "ركعتا الفجر خير من الدنيا وما فيها" أخرجه مسلم، صلاة المسافرين، حديث:725.»©Explanation:
➊ There is not the slightest room for doubt that the Prophet (sallallahu alayhi wa sallam) observed the two Sunnah (supererogatory) units (rak‘ahs) of Fajr, from among the regular Sunnah prayers (sunan rawatib), with such consistency that he did not show the same level of care for any other Sunnah prayers. He never abandoned them, whether at home or while traveling.
In view of the strong emphasis on these two Sunnah rak‘ahs, the Hanafis have even made it obligatory to perform them before the obligatory (fard) prayer, even if the congregational prayer (jama‘ah) has already commenced. However, this is explicitly contrary to the hadith, because it is not permissible to perform any other prayer when the congregational obligatory prayer is in progress. Thus, the statement of the Prophet (sallallahu alayhi wa sallam) is: «إِذَا أُقِیمَتِ الصَّلاَۃُ فَلَا صَلَاۃَ إِلاَّ الْمَکْتُوبَۃَ» “When the iqamah is pronounced (for prayer), there is no prayer except the obligatory prayer.”
(Sahih Muslim, Salat al-Musafirin, Chapter: The Dislike of Beginning a Voluntary Prayer..., Hadith: 710)

➋ The narration in al-Bayhaqi which states that when the congregation stands, there is no prayer except the obligatory prayer, except for the Sunnah of Fajr, is completely baseless and weak.
For details, see: (Awn al-Ma‘bud)