The identification and preservation of surahs during the Prophet’s lifetime form the starting point. The subsequent collection and safeguarding of the Qur’an associated with the periods of Abū Bakr and ʿUmar belong to the history of the written muṣḥaf.
Collecting the Qur’an and reorganizing it by subject are two different acts. Gathering the revealed text into a preserved written collection does not imply rearranging its teachings as a new topical manual. Preservation of the text and faithful transmission are the relevant concerns.
This distinction prepares for the discussion of the traditional divisions of the surahs and the dissemination of muṣḥaf copies in the period of ʿUthmān. Combining all these historical stages into one indistinct event would conceal their different purposes.