Of course in the Eastern Mediterranean, there was no "Dark Age" until the rise of Islam (though Greece itself outside the immediate orbit of Constantinople underwent one due to a Slavic invasion a bit later than the onset of the Western Dark Ages), and even then classical learning wasn't forgotten.
Not only were folks in the 6th century fully literate and conversant with classical literature as well as Scripture, the preservation of literacy and classical learning in the Empire persisted down until its fall in 1453, when the flight of Greek scholars to Venice and the surrounding region of Italy was the impetus for the Renaissance.
St. Photius the Great, Patriarch of Constantinople in the 9th century was a notable humanist, conversant with the pagan classics in literature and philosophy as well as Scripture and the writings of the earlier Church Fathers.
Anna Comnena's 11th century biography of her father the Emperor Alexis I, The Alexiad, is rife with classical allusions. (Note: at least in the greater houses, the women were both literate and well educated--indeed enough sources attest to women educating their children in grammar, that apparently literacy, though not formal education, seems to have been common among men and women in all strata of society.)
Then, too, there were suddenly Slavic speaking immigrants living in Greece itself, and throughout Anatolia, and absolutely no one bothered to make a record of their arrival, or to even appear to be interested in the phenomenon.
This is startling considering the vast sums the Eastern Empire had previously been spending to keep these people out!!!!
Fortunately there were enough people left so they could write about Justinian's Plague, and that, by itself, is remarkable since it left North Africa virtually unpopulated, and continental Western Europe simply disappeared as a place where humans lived.
China didn't bother to do anything for the next 500 years, not even trade luxury goods and gold with the Eastern Empire. The Silk Road simply disappeared and wasn't mentioned again for centuries.
But, there were bright spots. Mecca and Medina were relatively big time in that period, as was Petra ~ although the people there were incredibly poor, they were alive, had enough to eat, and actually managed to continue running a major site of religious pilgrimmage. They were even literate.
Imagine their surprise when shortly after Mohammad's death they were able to conquer the next nearest Byzantine province in a couple of days ~ and then roll on over everything but the old core area almost without resistance.
I think the fact that the good old boys in Mecca were able to absorb almost the entirity of the remainder of world civilization in a decade to be one which gives us an idea of exactly how terrible the Dark Age had been. It was bad; real bad; horrible; so bad that people forgot to write about it, even in the Eastern Mediterranean.
Byzantium's core area is frequently pointed to as an exception, and true enough the old city encompassed a vast area which was fully protected by walls. It also had on hand sufficient food for a 7 year siege. Since the events which precipitated the Dark Ages were of shorter duration, the city was able to survive and reassert order, although not to the degree it had before the Dark Ages.
We can envision Orthodox monks staring over the walls into the wilderness beyond writing down their thoughts about how red the sunsets were, and lo, and behold, we have such ancient documents available. On the other hand, the Byzantines did not, themselves, bother to take expeditions to the nether regions to see what had happened to everybody else. They had to wait centuries until new civilizations arose and folks from Venice could bring in mounted French knights to finally loot their precious city.