Chapter 5: Was the Qur’an collected into one book under Muhammad’s supervision?
No. The following hadith shows that before Muhammad died he had not collect the words of the Qur’an into one authorised book, nor had he commanded this to be done. It was his companions who decided to do this. They gathered together material from various sources and made their own collections.

Sahih Al Bukhari Vol 6 No. 509: Bk 66.8
https://sunnah.com/bukhari:4986
Narrated Zaid bin Thabit: Abu Bakr As−Siddiq sent for me when the people! of Yamama had been killed (i.e., a number of the Prophet's Companions who fought against Musailama). (I went to him) and found `Umar bin Al−Khattab sitting with him. Abu Bakr then said (to me), "`Umar has come to me and said: "Casualties were heavy among the Qurra' of the! Qur'an (i.e. those who knew the Qur'an by heart) on the day of the Battle of Yalmama, and I am afraid that more heavy casualties may take place among the Qurra' on other battlefields, whereby a large part of the Qur'an may be lost. Therefore I suggest, you (Abu Bakr) order that the Qur'an be collected." I said to `Umar, "How can you do something which Allah's Apostle did not do?" `Umar said, "By Allah, that is a good project. "`Umar kept on urging me to accept his proposal till Allah opened my chest for it and I began to realize the good in the idea which `Umar had realized." Then Abu Bakr said (to me). 'You are a wise young man and we do not have any suspicion about you, and you used to write the Divine Inspiration for Allah's Apostle. So you should search for (the fragmentary scripts of) the Qur'an and collect it in one book)." By Allah If they had ordered me to shift one of the mountains, it would not have been heavier for me than this ordering me to collect the Qur'an. Then I said to Abu Bakr, "How will you do something which Allah's Apostle did not do?" Abu Bakr replied, "By Allah, it is a good project." Abu Bakr kept on urging me to accept his idea until Allah opened my chest for what He had opened the chests of Abu Bakr and `Umar. So I started looking for the Qur'an and collecting it from (what was written on) palmed stalks, thin white stones and also from the men who knew it by heart, till I found the last Verse of Surat at−Tauba (Repentance) with Abi Khuza`ima Al−Ansari, and I did not find it with anybody other than him. The Verse is: 'Verily there has come unto you an Apostle (Muhammad) from amongst yourselves. It grieves him that you should receive any injury or difficulty..(till the end of Surat−Baraa' (at−Tauba) (9.128−129) Then the complete manuscripts (copy) of the Qur'an remained with Abu Bakr till he died, then with `Umar till the end of his life, and then with Hafsa, the daughter of `Umar.

Sahih Al Bukhari 9.301: Bk 93.53
https://sunnah.com/bukhari:7191
Narrated Zaid bin Thabit: Abu Bakr sent for me owing to the large number of casualties in the battle of Al−Yamama, while `Umar was sitting with him. Abu Bakr said (to me), `Umar has come to my and said, 'A great number of Qaris of the Holy Qur'an were killed on the day of the battle of Al−Yamama, and I am afraid that the casualties among the Qaris of the Qur'an may increase on other battle−fields whereby a large part of the Qur'an may be lost. Therefore I consider it advisable that you (Abu Bakr) should have the Qur'an collected.' I said, 'How dare I do something which Allah's Apostle did not do?' `Umar said, By Allah, it is something beneficial.' `Umar kept on pressing me for that till Allah opened my chest for that for which He had opened the chest of `Umar and I had in that matter, the same opinion as `Umar had." Abu Bakr then said to me (Zaid), "You are a wise young man and we do not have any suspicion about you, and you used to write the Divine Inspiration for Allah's Apostle. So you should search for the fragmentary scripts of the Qur'an and collect it (in one Book)." Zaid further said: By Allah, if Abu Bakr had ordered me to shift a mountain among the mountains from one place to another it would not have been heavier for me than this ordering me to collect the Qur'an. Then I said (to `Umar and Abu Bakr), "How can you do something which Allah's Apostle did not do?" Abu Bakr said, "By Allah, it is something beneficial." Zaid added: So he (Abu Bakr) kept on pressing me for that until Allah opened my chest for that for which He had opened the chests of Abu Bakr and `Umar, and I had in that matter, the same opinion as theirs. So I started compiling the Qur'an by collecting it from the leafless stalks of the date−palm tree and from the pieces of leather and hides and from the stones, and from the chests of men (who had memorized the Qur'an). I found the last verses of Sirat−at−Tauba: ("Verily there has come unto you an Apostle (Muhammad) from amongst yourselves−−' (9.128−129) ) from Khuza`ima or Abi Khuza`ima and I added to it the rest of the Sura. The manuscripts of the Qur'an remained with Abu Bakr till Allah took him unto Him. Then it remained with `Umar till Allah took him unto Him, and then with Hafsa bint `Umar.

Sahih Al Bukhari 6.515: Bk 66.15
https://sunnah.com/bukhari:4993
Narrated Yusuf bin Mahk: While I was with Aisha, the mother of the Believers, a person from Iraq came and asked, "What type of shroud is the best?" `Aisha said, "May Allah be merciful to you! What does it matter?" He said, "O mother of the Believers! Show me (the copy of) your Qur'an," She said, "Why?" He said, "In order to compile and arrange the Qur'an according to it, for people recite it with its Suras not in proper order." `Aisha said, "What does it matter which part of it you read first? (Be informed) that the first thing that was revealed thereof was a Sura from Al−Mufassal, and in it was mentioned Paradise and the Fire. When the people embraced Islam, the Verses regarding legal and illegal things were revealed. If the first thing to be revealed was: 'Do not drink alcoholic drinks.' people would have said, 'We will never leave alcoholic drinks,' and if there had been revealed, 'Do not commit illegal sexual intercourse, 'they would have said, 'We will never give up illegal sexual intercourse.' While I was a young girl of playing age, the following Verse was revealed in Mecca to Muhammad: 'Nay! But the Hour is their appointed time (for their full recompense), and the Hour will be more grievous and more bitter.' (5 4.46) Sura Al−Baqara (The Cow) and Surat An−Nisa (The Women) were revealed while I was with him." Then `Aisha took out the copy of the Qur'an for the man and dictated to him the Verses of the Suras (in their proper order) .