Aleyküm Selam!
The first thing to be noted in this regard is the promise of Allah is with the protection of the Quran, not the Hadith. Now as for the second part, yes, it is very true that the Hadith and Quran, both were transmitted through the Holy Prophet but the methodology is quite different.
The Quran was transferred with the ijma, tawater i e consensus of the Ummah, from one generation to the other as it is, just like the Sunnah (the actions of the Prophet peace be upon him), hence, we find no change in it.
Secondly, the journey of compilation of the Quran started in the time of the Prophet, where the revealed verses were not only being memorized by the disciples of the Prophet, but also written by various Sahabah, who were appointed by the Prophet (pbuh) for this very purpose, that are known as Katib-e-Wahi. Then the compilation in form of one book by Usma (R.A) and you can’t find any difference in the first and the last copy of Quran, till now so far…
As for the Hadith, it is a report, a historical piece of information that was not organized by the Prophet himself, but after His death, his companions quoted is sayings, incidents and actions… Later on they were scrutinized through (Asma-Rijal) but there is still a space of loop hole, due to the human reporters and the process…
So you can see, it is not only the Promise of Allah but the process initiated and completed in the very life of Prophet peace be upon him, that manifested as the promise completion of Allah… And it is not logical to fathom, billions of people agreed on a same, exactly same book, and that’s wrong
Unlike the Bible, the Quranic compilation and transfer is quite different, that closes any door for dispute or doubt…
Hope it’s satisfying
JazakAllah!