What is the hadith mentioned in the ibn Kathir tafsir on Quran 7:172-174?

Question

I'm trying to find the hadith mentioned in the ibn Kathir tafsir on Quran 7:172-174, which says

Quran 7:172-174 “When your Lord drew forth from the children of Adam - from their loins - their descendants, and made them testify concerning themselves, (He said), ‘Am I not your Lord?‘, they said, ‘Yes! We do testify!‘ Lest you should claim on the Day of Resurrection, ‘Truly, we were heedless of this.‘ Or lest you should claim, ‘Our fathers before us may have taken false gods, but we are their descendants after them. Will You destroy us because of what false and worthless men did?‘ Thus do We explain the signs in detail, that perchance they may return.”

The ibn Kathir tafsir for these verses states:

There are Hadiths that mention that Allah took Adam's offspring from his loins and divided them into those on the right and those on the left.

And then later states:

At-Tirmidhi said, "This Hadith is Hasan Sahih, and it was reported from various chains of narration through Abu Hurayrah from the Prophet ''. Al-Hakim also recorded it in his Mustadrak, and said; "Sahih according to the criteria of Muslim, and they did not record it.'' These and similar Hadiths testify that Allah, the Exalted and Most Honored, brought forth Adam's offspring from his loins and separated between the inhabitants of Paradise and those of the Fire.

What hadith is is the tafsir referring to, Hasan Sahih, reported through Abu Hurayrah? I also don't know what Mustadrak is, which is mentioned next.

On a related note, I was previously told about these related hadiths (I haven't verified these): Bukhari, Anbiya, 2; Muslim, Birr, 159; Abu Dawud, Adab, 19

That apparently say

“Souls are like crowds which gather together. The ones who met before get on well. The ones, who did not meet before, cannot get on very well and separate.”

My related question: When are souls created?

Answer 1

The english translation of Tafsir Ibn Kathir is abridged and omits some of the hadith cited after this sentence:

There are Hadiths that mention that Allah took Adam's offspring from his loins and divided them into those on the right and those on the left.

As for this sentence:

At-Tirmidhi said, "This Hadith is Hasan Sahih, and it was reported from various chains of narration through Abu Hurayrah from the Prophet ''. Al-Hakim also recorded it in his Mustadrak, and said; "Sahih according to the criteria of Muslim, and they did not record it.''

It is regarding the hadith that has been quoted just before it:

At-Tirmidhi recorded that Abu Hurayrah said that the Messenger of Allah said,

[ arabic text ]

(When Allah created Adam ...

... his offspring made mistakes.)

This is from Jami at-Tirmidhi, Kitab al-Tafsir, 3076 and has also been collected by al-Hakim Nishapuri in his Mustadrak ala al-Sahihain, Kitab al-Tafsir, Surah Al-A'raf, 3257. Mustadrak is a collection of hadith that the author claims to be Saheeh on the conditions of Bukhari and Muslim.