Bukhari

Hadith Commentary:
In the translation of the chapter, rent was mentioned, while in the hadith, phlegm is mentioned.
Since both are human excretions, the ruling for both is the same. In the mentioned hadith, there is no restriction regarding prayer.
However, further ahead, the same narration is coming from Adam ibn Abi Iyas, in which there is a restriction regarding prayer.
Imam Nawawi rahimahullah states that this prohibition is absolute.
That is, whether one is in prayer or not, whether in the mosque or outside the mosque, spitting in the direction of the qiblah is prohibited.
In the previous chapter, there was mention of cleaning the spit with one's hand, and here, scraping it off with a pebble is mentioned.
From this, it is evident that sometimes the Prophet sallallahu alayhi wa sallam did it this way, and sometimes that way; in both manners, the objective is to keep the mosque clean.

Hadith Commentary:
Shah Waliullah Muhaddith Dehlawi rahimahullah, in his explanation of the chapter headings of Bukhari, writes that with this chapter title, Imam Bukhari rahimahullah refutes those individuals who, based on the mentioned hadith, have argued that nasal mucus is impure. Their reasoning is that the Messenger of Allah sallallahu alayhi wa sallam personally performed this act not merely for the cleanliness of the mosque, but rather because he wished to purify the mosque from impurity. However, it is possible that Imam Bukhari rahimahullah’s intention was indeed to refute these individuals, because Imam Bukhari generally takes such matters into consideration in his chapter headings, and perhaps he mentioned the narration of Ibn Abbas radi Allahu anhu for this very purpose, as it serves to refute those people. But in my view, the best explanation is that when Imam Bukhari rahimahullah possesses a hadith through multiple chains of transmission, he does not mention all those chains in one place; rather, it is his habit to mention each narration under a separate chapter heading, and, taking into account the wording of the hadith, he introduces variety in the chapter titles and headings. The main objective is to mention the different chains of transmission of the hadith, otherwise the purpose of the chapter “Bab al-Buzaq” (Chapter on Spitting) and “Bab al-Mukhat” (Chapter on Nasal Mucus) is the same.

Sometimes, Imam Bukhari rahimahullah’s objective is not the chapters themselves, but rather the narrations. Thus, here too, the objective is not the chapters, but the narrations.

And Allah knows best.

Hadith Commentary:
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Imam Bukhari rahimahullah has mentioned in the chapter heading the prohibition of spitting to the right side during prayer, whereas the narrations are absolute (mutlaq); they do not specify the condition of prayer. However, in other narrations, the restriction of prayer is present.
As is found in Sahih Bukhari, the hadith of Anas 413 and the hadith of Abu Hurairah radi Allahu anhu 416; therefore, according to Imam Bukhari rahimahullah, these absolute narrations will be interpreted in light of the restricted narrations.
Is it permissible to spit to the right side outside of prayer or not? For this, other narrations must be consulted.
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Imam Nawawi rahimahullah has mentioned an absolute prohibition regarding this, whether one is in the mosque or outside the mosque, in prayer or outside of prayer.
Thus, the prohibition has been transmitted from numerous predecessors (salaf).
As is narrated from Abdullah ibn Mas’ud radi Allahu anhu that he declared spitting to the right side to be prohibited even outside of prayer. Hazrat Mu’adh ibn Jabal radi Allahu anhu said: “Even after accepting Islam, I have never spat to the right side.”
Hazrat Umar ibn Abdul Aziz rahimahullah absolutely forbade his son from spitting to the right side.
Those who restrict the prohibition to the state of prayer, their evidence is probably the narration in which it is mentioned that during prayer, there is an angel on the right side.
(Sahih al-Bukhari, Kitab al-Salat, Hadith: 416)
This would be in the case where, apart from the angels who watch over and record good deeds, another angel is intended, because the watchers and the noble scribes (kiraman katibin) are always present on the right side.
(Fath al-Bari: 1/661)
Imam Bukhari rahimahullah, by adding the phrase “during prayer” (fi al-salat) in the chapter heading, has supported Imam Malik rahimahullah, because according to him, this prohibition is specific to prayer.
According to us, the position of Imam Bukhari rahimahullah is the preferred one, because during prayer, Allah ta’ala appoints an angel on the right side of the worshipper who protects his heart; therefore, during prayer, spitting to the right side is prohibited and to the left side is permissible.
It should be noted that the worshipper is permitted to spit to the left side only when there is no worshipper on his left, as will be clarified in the following hadith. It is well known regarding the permissibility of spitting to the left side that the Shaytan is on the left side, who casts whispers into the heart; this spit falls on the head of Shaytan and thus becomes a means of his humiliation and disgrace.
The basis of this explanation is a narration which, although well-known, is in fact very weak; see:
Al-Mu’jam al-Kabir by al-Tabarani rahimahullah 8/199, Hadith number: 7808, second edition.

Hadith Commentary: Benefits and Issues: If a person is alone, he may spit to his left outside the mosque. If there is another person present on his left side, then he should spit beneath his left foot.