Bulugh al-Maram

Linguistic Explanation:
«اَلنَّعْيِ» Giving news of death. Merely informing to the extent that people may participate in the deceased’s shrouding, burial, and funeral prayer is not prohibited. However, announcing in the manner of the Age of Ignorance (Jahiliyyah) is prohibited. Its nature was such that in this announcement there would be wailing, and the deeds of the deceased would be recounted in a boastful manner while roaming through markets and streets.

Benefit: Our esteemed researcher has declared the aforementioned narration weak in its chain of transmission; however, in light of other hadiths, merely informing of a death is not absolutely prohibited. For example, when Najashi rahimahullah passed away in Abyssinia, the Messenger of Allah sallallahu alayhi wa sallam informed the Companions in Madinah and performed the absentee funeral prayer (salat al-janazah) for him. Furthermore, in the Battle of Mu’tah, when Zayd, Ja’far al-Tayyar, and Abdullah ibn Rawahah radi Allahu anhum were martyred one after another while leading the Muslims, the Messenger of Allah sallallahu alayhi wa sallam was informed through revelation, and he immediately informed the Companions radi Allahu anhum in Madinah of their martyrdom. See: [صحيح البخاري الجنائز ، حديث : 1245]
Therefore, the prohibition in the aforementioned narration refers to that Jahiliyyah-style announcement, where, when a person died, a few individuals would be appointed to roam the markets and streets, announcing his death with wailing and recounting his deeds and virtues in a boastful manner. And Allah knows best.

Benefits and Issues:

➊
In the era of ignorance (Jahiliyyah), it was customary that when a person died, several individuals would be appointed to roam around the markets and streets, announcing his death while weeping and wailing.
The more important the deceased was, the greater the arrangement made for this.
This was called "na‘yi" (public announcement of death).

➋
It is permissible to inform one another in a simple manner,
so that people can make arrangements for his shrouding and burial, and participate in the funeral prayer (salat al-janazah).
When Najashi (the Negus) passed away in Abyssinia,
the Messenger of Allah (sallallahu alayhi wa sallam) informed the noble Companions (radi Allahu anhum ajma‘in) in Madinah,
and performed the funeral prayer in absentia (salat al-janazah al-gha’ib).
In addition, during the Battle of Mu’tah, Zayd, Ja‘far al-Tayyar, and ‘Abdullah bin Rawahah (radi Allahu ta‘ala anhum) were successively martyred while leading the Muslim army.
The Messenger of Allah (sallallahu alayhi wa sallam) was informed of this by revelation, and at that time in Madinah, he informed the noble Companions (radi Allahu anhum ajma‘in) of their martyrdom.
See: (Sahih al-Bukhari, al-Jana’iz, Chapter: A man announcing the death to the family of the deceased himself, Hadith: 1246, 1245)
After the martyrdom of ‘Abdullah bin Rawahah (radi Allahu ta‘ala anhu) in this battle, Khalid bin Walid (radi Allahu ta‘ala anhu) took command of the Muslim army and returned successfully.
On this occasion, the Messenger of Allah (sallallahu alayhi wa sallam) referred to Khalid bin Walid (radi Allahu ta‘ala anhu) as the Sword of Allah, and thus his title "Sayf Allah" became well-known.

➌
According to some, this narration is hasan (good).
And in this as well, the prohibition refers to that Jahiliyyah-style announcement, the details of which have been clarified in the above lines.