Bukhari

(Hadith Commentary:
Sitting during the middle of the Friday sermon (khutbah) is also a Sunnah practice.)

Hadith Commentary:
(1)
Allamah Zayn ibn Munir rahimahullah has said that from the chapter heading established by Imam Bukhari rahimahullah, the ruling of sitting between the two sermons does not appear to be obligatory, because the evidence and reliance for this action is the Prophetic practice (fi‘l al-nabawi), and an action (fi‘l) does not entail general applicability.
The author of Al-Mughni has written that most of the scholars have not considered it obligatory, as there is no prescribed dhikr or the like in it.
Those who hold it to be obligatory, according to them, its duration is like the sitting of rest (jalsat al-istirahah), or as long as it takes to recite Surah al-Ikhlas.
(Fath al-Bari: 2/522)
(2)
There is some detail in the narration of Sunan Abu Dawud, whose wording is as follows:
The Messenger of Allah sallallahu alayhi wa sallam would deliver two sermons.
When he ascended the pulpit, he would sit until the mu’adhdhin finished the adhan.
Then he would stand and deliver the sermon, then sit and not speak or anything, then stand and deliver the sermon.
(Sunan Abi Dawud, al-Salat, Hadith: 1092)
From this narration, it is understood that during the sitting, the imam should not engage in any kind of conversation; however, silent dhikr is not prohibited.
And Allah knows best.

Hadith Commentary:
The Shafi'is have stated that standing (qiyam) is a condition for delivering the sermon (khutbah), because the Noble Qur'an says: ﴿وَتَرَكُوكَ قَائِمًا﴾ (al-Jumu'ah: 11),
and it is established from the hadiths that the Prophet (sallallahu alayhi wa sallam) always delivered the sermon while standing.
When Abdur Rahman ibn Abi al-Hakam was delivering the sermon while sitting, the Companion Ka'b ibn Ujrah (radi Allahu anhu) objected to this.

Hadith Commentary:
If it were permissible to deliver the Friday sermon while sitting, then what significance would remain for sitting between the two sermons? Furthermore, the meaning of the Qur’anic verse ﴿وَتَرَكُوكَ قَائِمًا﴾ also necessitates that the Friday sermon be delivered while standing.

This is further clarified by the following hadith, which states that the Messenger of Allah (sallallahu alayhi wa sallam) used to deliver the Friday sermon while standing: Once, during the sermon, a trade caravan arrived from Syria. When the people found out, they left the sermon and went towards it, until only twelve men remained. At that moment, the verse ﴿وَتَرَكُوكَ قَائِمًا﴾ was revealed.
(Sahih al-Bukhari, al-Jumu‘ah, Hadith: 938)

In addition, it is narrated from Jabir ibn Samurah (radi Allahu anhu) that the Messenger of Allah (sallallahu alayhi wa sallam) used to deliver the sermon while standing.
Whoever says that he (sallallahu alayhi wa sallam) delivered the sermon while sitting has lied.
By Allah! I have prayed more than two thousand prayers with him.
(Sahih Muslim, al-Jumu‘ah, Hadith: 1996 (862))

However, if there is an excuse, then the sermon may be delivered while sitting, as is mentioned in a narration that Mu‘awiyah (radi Allahu anhu) had an increase of fat and flesh in his belly, so he delivered the sermon while sitting.

For sermons other than the Friday sermon, it is permissible to deliver them while sitting.
As Abu Sa‘id al-Khudri (radi Allahu anhu) states that the Messenger of Allah (sallallahu alayhi wa sallam) one day sat on the pulpit (to deliver an admonition), and we also sat around him.
(Sahih al-Bukhari, al-Jumu‘ah, Hadith: 921)

Hafiz Ibn Hajar (rahimahullah) has transmitted from Musannaf ‘Abd al-Razzaq a hadith that the Messenger of Allah (sallallahu alayhi wa sallam), Abu Bakr (radi Allahu anhu), ‘Umar (radi Allahu anhu), and ‘Uthman (radi Allahu anhu) used to deliver the Friday sermon while standing, until it became difficult for ‘Uthman (radi Allahu anhu) to deliver the sermon while standing, so he would sit down while standing.

Regarding Mu‘awiyah (radi Allahu anhu), it is also narrated that he would deliver the first sermon while sitting and stand for the second.

These incidents are not evidence for delivering the sermon while sitting, because such was done out of necessity.
(Fath al-Bari: 2/516)

Once, Ka‘b ibn ‘Ujrah (radi Allahu anhu) entered the mosque and saw ‘Abd al-Rahman ibn Umm al-Hakam delivering the Friday sermon while sitting.
He objected to this action and recited the verse ﴿وَتَرَكُوكَ قَائِمًا﴾.
(Sunan al-Nasa’i, al-Jumu‘ah, Hadith: 1398)

1092. Commentary:
➊ It is recommended (mustahabb) to deliver the sermon (khutbah) of Jumu'ah while standing on the pulpit (minbar). Without a valid excuse, delivering the sermon while sitting is impermissible. The sitting of the Prophet sallallahu alayhi wa sallam between the two sermons used to be very brief.
➋ The sermons, in terms of number, are two—not three. Any speech or address before the prescribed sermons increases this number, and therefore it is not permissible. This is a deviation from the Sunnah of the Messenger sallallahu alayhi wa sallam, whereas the need is to act upon the Sunnah of the Messenger sallallahu alayhi wa sallam.

Benefits and Issues:

➊ There are two sermons (khutbahs) for Jumu‘ah (Friday prayer).

➋ The sermon should be delivered while standing, except if there is a valid excuse.

➌ To separate the two sermons, one should sit for a short while.

➍ In both sermons, admonition and advice should be given. Jabir bin Samurah radi Allahu anhu said: The Noble Prophet sallallahu alayhi wa sallam used to deliver two sermons, and he would sit between them. In the sermons, he would recite the Noble Qur’an and advise the people. (Sahih Muslim, al-Jumu‘ah, Chapter: Mention of the Two Sermons before the Prayer and What is in Them of Sitting, Hadith: 862)