Bukhari

Hadith Commentary:
At such a delicate time, it was only Abu Bakr radi Allahu anhu who was able to steady the Ummah.
This is why the Messenger of Allah sallallahu alayhi wa sallam, before his passing, appointed him as his successor by making him the Imam of prayer, which is a clear proof of his rightful caliphate.
Abu Bakr radi Allahu anhu, by saying that Allah will not cause you to die twice, refuted those Companions radi Allahu anhum who thought that the Prophet sallallahu alayhi wa sallam would come back to life and cut off the hands and feet of the hypocrites, because if that were to happen, then death would occur again, as if there would be two deaths.
Some have said that the meaning of "not dying twice" is that there will not be another death in the grave, rather, you will remain alive.
In the narration of Imam Ahmad, it is stated that Aisha radi Allahu anha says: When the Messenger of Allah sallallahu alayhi wa sallam passed away, I covered him with a cloth.
After that, Umar radi Allahu anhu and Mughira radi Allahu anhu came.
Both sought permission to enter.
I granted them permission.
Umar radi Allahu anhu, upon seeing the body, said, "Alas, you have become unconscious."
Mughira radi Allahu anhu said, "He has passed away."
At this, Umar radi Allahu anhu rebuked Mughira radi Allahu anhu, saying that the Messenger of Allah sallallahu alayhi wa sallam will not die until all the hypocrites are eradicated.
In another narration, it is stated that Umar radi Allahu anhu was saying, "Beware! Whoever says that the Messenger of Allah sallallahu alayhi wa sallam has died, I will strike off his head with the sword."
Umar radi Allahu anhu truly believed that the Messenger of Allah sallallahu alayhi wa sallam had not died, or his saying this was based on great wisdom and political insight.
He intended that first the matter of the caliphate should be settled, and only then should the news of the Prophet's passing be made public, lest hearing of his death cause any harm to the religion.

Hadith Commentary:
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At the passing of the Messenger of Allah (sallallahu alayhi wa sallam), the people of Madinah were overcome with great distress, to the extent that even a steadfast figure like Umar (radi Allahu anhu) lost his senses.
He stood with his sword unsheathed and said, “Whoever says that the Messenger of Allah (sallallahu alayhi wa sallam) has passed away, I will strike off his neck.”
Hafiz Ibn Hajar (rahimahullah), referencing Musnad Ahmad, has written that when the Messenger of Allah (sallallahu alayhi wa sallam) passed away, Aisha (radi Allahu anha) covered him with a cloth.
After this, Umar (radi Allahu anhu) and Mughira ibn Shu’bah (radi Allahu anhu) came and both sought permission to enter.
Aisha (radi Allahu anha) granted them permission. Umar (radi Allahu anhu), upon seeing him, said:
“Alas! You have fallen unconscious.”
Mughira (radi Allahu anhu) said:
“You have passed away.”
At this, Umar (radi Allahu anhu) rebuked him, saying:
“You are mistaken and have fallen into a trial (fitnah).
The Messenger of Allah (sallallahu alayhi wa sallam) will not pass away until all the hypocrites have been eliminated.”
After this, Abu Bakr (radi Allahu anhu) arrived, lifted the veil and looked at him, recited: “Inna lillahi wa inna ilayhi raji’un,”
and said:
“The Messenger of Allah (sallallahu alayhi wa sallam) has passed away.”
(Musnad Ahmad: 219/6)

➋
Abu Bakr (radi Allahu anhu) used the noble name “Muhammad” instead of “Messenger of Allah” (Rasul Allah) because the intent was to refer to the blessed person himself.
Saying “Messenger of Allah” draws attention to the attribute of messengership (risalah), whereas at that moment, the attribute of messengership was not the focus, since it pertains to the One Who sent (i.e., Allah, the Exalted), and that connection had not been severed. If his messengership had been severed, then mentioning the noble person would not have been appropriate. Therefore, instead of the attribute of messengership, the noble name was mentioned.
And Allah knows best.