So the interpretation of "there is no Prophet after me" is "there is no Prophet after me" (in my nation) or (among my twelve successors)?
Why didn't the Prophet say this? Why didn't he just say the additional words?
Good question. I am always fine with challenging and fair questions.
We will look at various Hadithes.
First, we can only accept hadithes which are compatible with Quran. Hadith authenticity must be weighed against Quran, by finding parallels with a verse.
Here are some hadithes related to this discussion:
The tribe of Israel was guided by prophets. When a prophet passed away, another prophet succeeded him. But no prophet will come after me; only caliphs will succeed me.
(Bukhari)
So, the above Hadith which says no prophet after Muhammad is about successorship. Because it is making a comparison with prophets of Israel, who were successors of Moses. It is an authentic hadith, as Quran confirms prophets of Israel as successors of Moses.
Here is another Hadith:
You (Hazrat Ali) are related to me as Aaron was related to Moses (pbuh). But no Apostle will come after me.
(Bukhari, Muslim)
The above Hadith is about immediate successorship, for it is making comparison to Moses and Aaron who lived in the same time. Likewise Muhammad and Ali.
Here are other Hadithes that is Not about immediate successorship, but we will see what they are about:
Allah's Messenger (ﷺ) said, "My similitude in comparison with the other prophets before me, is that of a man who has built a house nicely and beautifully, except for a place of one brick in a corner. The people go about it and wonder at its beauty, but say: 'Would that this brick be put in its place!' So I am that brick, and I am the last of the Prophets."
The chain of Messengers and Prophets has come to an end. There shall be no Messenger nor Prophet after me.
(Tirmidhi, Musnad Ahmad, Anas bin Malik)
These Hadithes are talking about a chains of Messengers who started with Adam and ended with Muhammad. This hadith is likening creation of humanity as a building. It started with Adam and Ended.
This is known as the first creation in the Quran. But, since God is always a creator, after this first creation, He will start a later creation, which is stated in the Quran:
“Are We wearied out with the first creation? Yet are they in doubt with regard to a
new creation!”
This verse tells us, that after first creation, there will be a new creation. This new creation, starts by the Qaim, who is a Messenger with a new Book according to traditions.
What is this new creation? In scriptures, it is known as creating of a new earth. How a new earth looks like, it is in this verse:
“Know that Allah gives life to the earth after its death; indeed, We have made the communications clear to you that you may understand.” (Surah Hadid 57:17)
In Ghaibat of Shaykh Tusi through the same chain of narration from Ibne Abbas about the verse it is narrated that he said: “It means that the earth will be restituted through the Qaim of Aale Muhammad (a.s.) after its death, that is, after the inequity of its rulers. We explained to you the signs, through the Qaim of Aale Muhammad (a.s.), so perhaps you may understand.”
So, based on the above hadithes, there was a first creation of earth, which is likened to a building block. Muhammad was the last brick of this first creation. Then Allah sends Qaim, for creation of a new earth. In another words, Muhammad was the Last Messenger of the first creation! The new creation has it's own Messengers, beginning with the Qaim.