Bukhari

Hadith Commentary:
Perhaps Imam Bukhari rahimahullah derived the purpose of the chapter from this hadith in such a way that since these days are days of happiness for every individual, therefore, every person must also perform the Eid prayer.

The Messenger of Allah sallallahu alayhi wa sallam declared the day of Eid al-Adha and the subsequent days of Tashreeq—the eleventh, twelfth, and thirteenth—all as days of Eid, and stated that firstly, the day of Eid itself is a day of happiness, and then there is additional joy in Mina because Allah granted the blessing of Hajj.

Hadith Commentary:
(1)
Regarding the relevance of these ahadith to the chapter heading, Ibn Munir has written that Imam Bukhari rahimahullah has deduced from the words "Innaha ayyam ‘id" ("These are days of ‘Eid") because in these words, the attribution of ‘Eid is made to the days in an absolute sense. Therefore, for the establishment of the ‘Eid prayer, whether individually, in congregation, for women or men, all are equal.
Then Ibn Rashid, furthering Ibn Munir’s point, has written that these are days of ‘Eid for the people of Islam.
As is mentioned in another hadith: "O people of Islam! These are our days of ‘Eid."
The words "people of Islam" include both individuals and congregations. However, for the making up (qada) of the ‘Eid prayer, Imam Bukhari’s reasoning is from the statement "the days of Mina are all days of ‘Eid."
When these days are called days of ‘Eid, then these days become the occasion for performing the ‘Eid prayer, because the legislation (mashru‘iyyah) of this prayer is based on the day of ‘Eid.
From this, it is understood that the ‘Eid prayer can be performed until the last day of the days of Mina.
(Fath al-Bari: 2/612)
And Allah knows best.
In summary, Imam Bukhari rahimahullah has deduced from the generality of this narration that when ‘Eid is for everyone, then the ‘Eid prayer is also for everyone, whether they are city dwellers or villagers, men or women.
(2)
At the end of the hadith, the word "amna" is said to be derived from "aman" (safety/security).
Its meaning is that it is not derived from "aman" (protection/guarantee), because the word "aman" is used for disbelievers and polytheists. If it were derived from "aman" (protection), then the joys of ‘Eid would be for everyone, whether they are polytheists or disbelievers.
The purpose of deriving it from "aman" (safety/security) is that ‘Umar radi Allahu anhu had rebuked and frightened the people of Habasha (Abyssinia), so the Messenger of Allah sallallahu alayhi wa sallam, rectifying this, said: Let them remain in a state of safety; let them do what they are doing. That is, O Banu Arfidah! Continue playing in peace and tranquility.