The hadith has been classed as Daeef by some such as al-Arnaa’oot in his grading of Sunan Abu Dawud and has been classed as Hasan by others such as by al-Albani in Irwa’ al-Ghaleel.
Within its chain, a transmitter of interest is Hisham bin Sa'd al-Madni - he has been weakened by a group of the Imams including Ahmad ibn Hanbal, Ibn Ma'in, Nasa'i, Abu Hatim, Ibn Saad, Ibn Hibban etc. However some have accepted his narrations on the condition that they be corroborated by others, so for example Imam Muslim has cited reports from him when they are supported by other evidence.
In this case, the main content of the hadith (the event of stoning of the adulterous Jews) is supported by several other sahih narrations, however the specific statement of the Prophet ﷺ regarding the written copy of the Torah is unique to this one.
Does the hadith say that Torah Has Not Been Corrupted?
One must understand what is meant by the Islamic creed of تحريف (distortion) the Torah. There are multiple madhabs on this, two major ones being:
The hadith does not conflict with either madhab. It is obvious how it is compatible with the second madhab, as for the first one:
The Prophet's saying:
آمنت بك وبمن أنزلك
I believed in thee and in Him Who revealed thee
Is directed towards the Torah, which was written inside the mushaf. Specifically to the lines on the law of Rajm. There may also be other text written elsewhere inside the mushaf but the Prophet ignored that and addressed the significant part. This is no different from the verses of the Quran which relate to the Torah such as:
وكيف يحكمونك وعندهم التوراة فيها حكم الله
But how is it that they come to you for judgement while they have the Torah, in which is the judgement of Allah?
— Quran 5:43
قل فأتوا بالتوراة فاتلوها إن كنتم صادقين
Say, [O Muhammad], "So bring the Torah and recite it, if you should be truthful."
— Quran 3:93
وقد استدل به بعضهم على أنهم لم يسقطوا شيئا من ألفاظها كما يأتي تقريره في كتاب التوحيد والاستدلال به لذلك غير واضح لاحتمال خصوص ذلك بهذه الواقعة فلا يدل على التعميم وكذا من استدل به على أن التوراة التي أحضرت حينئذ كانت كلها صحيحة سالمة من التبديل لأنه يطرقه هذا الاحتمال بعينه ولا يرده قوله آمنت بك وبمن أنزلك لأن المراد أصل التوراة
— Fath al-Bari