I mean the Russian Empire was fundamentally different from the Eastern Roman Empire in structure, culture, and society. The Bulgarian revolts of the Asen dynasty that established the Second Bulgarian Empire was more or less a tax revolt. The Asens petitioned the Angeloi for a Pronoia. The Angeloi not only refused but insulted the Asens which prompted them to revolt. With their ineptitude they they created an extortionate tax scheme that alienated much of Bulgaria and the rest of the population of the Empire. The Asens tapped into this to create the Second Bulgarian Empire. Previous Bulgarian revolts were largely put down with native Bulgarian troops.However not sure if I agree that the Romans will be entirely or even strongly successful in assimilation policies. For example counter them with the Russian Empire who IIRC did not majorly discriminate between subjects to the Tsar (provided they were loyal) and tried to assimilate people. But in the end failed with even the most similar groups like the Ukranians and Belorussians, though they came close. Where they had most success were disparate tribes, mainly from Ugro-Finnic types, so I guess the bigger the group the more they will present a challenge, with similarity to target group also being an issue.
Also the Eastern Roman state was fundamentally different from the Russian Empire in society, government, and culture. The Serbians and Bulgarians were part of the Orthodox Eastern Mediterranean world similar to how the Franks/French functioned with the West. Had Karolyan or the Second Bulgarian Empire at another point taken Constantinople, its likely that the Bulgarians would have been Hellenized/integrated into the Roman state. The Bulgarians with Constantinople and the rest of the Balkans could have mobilized troops to then fight the Turks in Anatolia. The Serbian Empire after the Second Palaiologian Civl War also could of done something similar. Serbian artwork during that time period reflected Medieval Eastern Roman art styles of well with Stefan IV Dusan "The Strong" stylizing himself as Emperor of the Serbs and the Romans.
The Romans were certainly brutal if that's what it took. A common joke about the Romans I heard in my history class is that the Romans were progressive because they "oppressed everyone even."You can't really do much about racial differences without some truly heavy handed policies but they are not big enough to be a roadblock like in the US, just a speedbump.
The Romans can't exert direct control everywhere. Some autonomous solutions might be available with something like a Despotate being created in Egypt. The Copts might actually prefer rule by the Romans over rule by the Mammaluks who began persecuting them and kicked the "Islamization" of Egypt into high gear.Ultimately I do not see major groups like the Copts assimilating, they are just too many to be ground down. Provided they were not fiercely pressured to convert or just expelled some Sunnies will stay too, same with Turks. Slavs in the Balkans as well probably. It is not impossible, but it will take a lot of effort on multiple fronts as I outlined, it would be a project that would take centuries.
The Age of Nationalism unfolded in the way it did due to a specific set of circumstances. Austria-Hungary almost emerged as a premier example of a successful multi-ethnic state. Had the Empire made it out of WWI, a new national identity based on common loyalty to the Habsburg dynasty would have emerged rather than being based on ethnic and linguistic grounds. Most of the population and large segments of the army were loyal to Franz-Joseph who was seen as a father to the nation due to his long reign. His death was a huge blow to the integrity of the Empire. Hungary during the interwar period and the duration of WWII was officially a Kingdom under a regency. Had a few things gone differently, Kaiser Karl I would have re-emerged as King of Hungary, and likely could have retaken Austria creating a rump Austria-Hungary as a counter-weight to Germany in WWII. Had the Sixtus Affair been a success, Austria-Hungary would have emerged intact but in a reduced form after the War.If you want an Empire that survives the Age of Nationalism more or less intact it simply needs a lot of unity in multiple layers. Or that is my thinking anyway, maybe you disagree.
I respectfully disagree with you here as comparing the development of the US government and Eastern Roman Empire is like comparing apples to oranges.And ultimately the USA was not that good at assimilation, they only really fully unified white protestants all other groups remained distinct to a degree. If you want an Empire that survives the Age of Nationalism more or less intact it simply needs a lot of unity in multiple layers. Or that is my thinking anyway, maybe you disagree.