I don’t know about that, the Eastern Roman Empire was the seat of the most advanced scholars and civilization outside of China until pretty much the very end of its days.
Something people often forget about the “Dark Ages” and the Roman Empire is that under Rome, Western Europe was by and large just as backward compared to the regions in the Eastern half of the Empire as it was during the dark ages. The dark ages didn’t really cause a “backward step” in technology and civilization for Western Europe as is often assumed.
The way to look at it instead is prior to the Roman Empire Greek culture spread throughout the Eastern Mediterranean. You had it intermixing with local cultures throughout the Levant, and specifically you had Greek monarchs in Egypt and even the pre-Roman Levantine had the Seleucid Empire. These were by far much more culturally and scientifically advanced states than anywhere else in that part of the world. Alexandria was a famous center of learning and several major cities in the Seleucid Empire had much more going in vis-a-vis scholarship than anywhere in Western Europe.
What changed with the Roman Empire is basically a Latin speaking Empire was overlayed on top of all that, but didn’t supplant or disrupt it. In fact the Romans adopted and studied a lot of the same stuff the Hellenistic cultures were studying. In Western Europe, this Latin Empire put its imprint on the top of society. Roman colonies or “Roman Towns” were built across Gaul, Hispania, and Britannia for sure, but by and large the peoples in those regions remained the same as they always were: illiterate, backward, and lacking in any major cultural or scientific centers.
When the Western Empire fell they lost their overlord, but pretty much kept going just as they always had technologically. I think a big part of the reason people see the Dark Ages as a retrenchment for Western Europe is because they do not understand that the Roman Empire wasn’t scholastically, intellectual, and scientifically homogenous. Rome was a massive city that certainly became a center of learning and science in its own right, but aside from that Western Europe was the backward part of the Roman Empire. The Hellenistic tradition never spread into the peoples of Western Europe aside from among the Roman upper classes that might move into those regions to administer them.
When the Muslim Empire started sweeping away everything before it in the Eastern Mediterranean in the 700s-1400s their society built on what was there before. They didn’t abandon the mathematics, science and etc of the peoples they were conquering, but built on them. Meanwhile Western Europe continued being more or less as backward as it always had been.
Something that is probably very important in explaining why Europe is not Muslim today is in fact the Roman Empire. The “Byzantines” as modern historians called them, were too powerful to be swept away. It basically took 700 years to conquer them, and that long period of being a bulwark in the East gave Europe the time it needed to advance to a point where it was too hard of a nut to crack for the powerful Muslim forces that had large organizational and technological advantages.
Europe steadily advanced technologically throughout the “Dark Ages” and Early Middle Ages, especially in areas of construction and military weaponry. In the Renaissance the Europeans basically imported all the ideas that up to then had only been studied in the Near East and in a few generations had wiped out much of the knowledge imbalance between them and the Muslim states. In the Enlightenment the Europeans came upon the scientific method and the pursuit of knowledge as more than just a pastime for the wealthy upper class but as a societal goal. This lead directly to basically all the major innovations that caused Europe to significantly outpace the rest of the world technologically.
Specifically as to Eastern Europe, I don’t see how it was stifled by being under Roman rule. Especially since in Constantinople you had by far the most educated, sophisticated city in all of Christendom probably even up until its conquest. I think Eastern Europe just had many of the same problems that Western Europe did, and simply didn’t benefit from their more sophisticated overlords. They also were the battleground for a large degree of warfare and religious conversiosn which lead to deep seated problems between warring religious groups. Eastern Europe had to deal with Ottoman invasions, Mongol invasions, and the Ottoman invasion in particular created a lot of Muslims in Eastern Europe that didn’t get along with the Christians in Eastern Europe which made it a very unstable place.