This is kind of a complicated question, but in short it depends on the specific hadith and the person reading it. The classical compilers were mostly interested in being as comprehensive as possible, collecting every transmission of every saying they could, without regard for reliability. However, because reliability was kind of important when determining how authoritative a hadith was, they also developed various "ratings" based on criteria like how many people transmitted the hadith, were those transmitters reliable, is the text of the hadith consistent with other versions from other transmitters, etc. A hadith from one single transmitter known to be "iffy" that had a text greatly at odds from other similar ahadith would be rated a lot lower than one from a large number of trustworthy transmitters who all passed on essentially the same text as each other, for instance.
The big famous collections of ahadith were basically later classical scholars attempting to sort through the vast amount of transmissions and texts and trying to pick just the best or most reliable )in their opinion). In Sunni Islam, there are the "Big Six" (which include Sahih al-Bukhari and Sahih Muslim), as well as a bunch of other, "lesser" collections. Shia Muslims have their own collections and do not consider the same ahadith and collections to be authoritative that Sunnis do, for complicated reasons that have to do with which transmitters supported which side in the First Fitnah and who is considered an "Imam" in Shia Islam (which is not the same as someone considered an "imam" in Sunni Islam).
As for the particular works cited by this dipstick, Siyar A’lam an-Nubala’ by al-Dhahabi is a collection of "historical" biographies of famous Islamic figures written in Syria in the medieval period, and the volume and page cited are to Imam Shaf'i, founder of the Shafi'i madhab of Sunni Islam, supposedly saying of the time when he lived (several centuries after Muhammad):
"I have seen many girls in Yemen undergo menses (reach the age of puberty) at the age of nine."
The second work is a book of ahadith (though not one of the major "authentic" collections in either Sunni or Shia Islam), compiled about 400 years after Muhammad, which is also attributed to Shafi'i (who, while respected, was not Muhammad and was not even a Companion) and reads:
"In San‘aa’ [in Yemen] I saw a grandmother who was twenty-one years old; she reached puberty at the age of nine and gave birth at the age of ten, and her daughter reached puberty at the age of nine and gave birth at the age of ten."
Considering these are both supposedly from the same person and relate similar things, they're probably just two different transmissions of the same commentary. They're also, you will note, about completely anonymous people from several hundred years before they were documented (and over a thousand years before today), in one small area of the Arabian peninsula.
So as "historical documents" go, they're aomewhat lacking, shall we say.