Abu Dawud

Hadith Commentary:
➊
In the title, the mention of saliva (spit), and in this narration, the mention of phlegm, Imam Bukhari rahimahullah intends to establish that saliva, phlegm, and nasal mucus, etc., are all unpleasant and repugnant things. The ruling regarding these undesirable things in the mosque is the same.
(Fath al-Bari: 1/661)

➋
In this narration, the words about spitting to the left, Imam Bukhari rahimahullah has indicated towards a difference of opinion.
According to Qadi Iyad rahimahullah, spitting in the mosque is permissible, but not burying it is a sin, whereas Imam Nawawi rahimahullah says that spitting in the mosque is a sin, and burying it is the expiation for that sin.
From the title established by Imam Bukhari rahimahullah, there is an indication towards the preponderance of Qadi Iyad’s position.
And Allah knows best.

➌
By quoting a chain of narration at the end, Imam Bukhari rahimahullah has also clarified that although the narration is transmitted with the wording “from” (an), the hearing (sama‘) of Imam Zuhri rahimahullah from his teacher Humaid ibn Abd al-Rahman is established; therefore, there is no suspicion of tadlis (concealment in transmission) in this.

726. Commentary: Spitting to the right is prohibited because on the right side is the angel of mercy, and spitting to the left is permissible only when there is no one else on that side, as that would be their right side. Alternatively, one may spit beneath one’s foot. The statements of the Prophet (sallallahu alayhi wa sallam) should be understood as referring to those mosques where the ground was unpaved, so that after spitting, it would be easy to bury it, and no one would be harmed by it. That is, those specific circumstances should also be kept in mind in which such rulings were issued. Nowadays, almost all or most mosques are constructed with solid flooring, and in fact, marble is often laid on the floors. Furthermore, there are some mosques where mats are spread, or in some cases, the entire mosque is covered with fine and exquisite carpets. In such places, spitting is certainly inappropriate and, in fact, extremely distressing for all the people of the mosque. It is possible that, considering future circumstances, the Prophet (sallallahu alayhi wa sallam) instructed to spit into a cloth and rub it. In the present day, this method should be adopted so that the need is fulfilled and the mosque remains clean. (See also, Hadith: 724)