sorry but i thought you were because of this statement:They're apparently saying they're indistinguishable from the surrounding people,so not descended from Byzantine Greeks.
sorry again but i am biased because i know from personal experience that south italians even if they are fully embracing their ancient greek past tend to think byzantines more like conquerers rather than a part of their ancestry that they should be proud of.
That may just be the people to whom you speak.
My husband is southern Italian, was a Classics student at university, and has some ancestors who spoke Grecanico and were Greek Orthodox until a few centuries ago. He's proud of all of it. My region of Italy was part of the reconquest only for a short period of tlme, but in eastern Italy, like Ravenna, for example, the Empire left a rich patrimony.
The fact remains, however, that the Empire was, in some sense, a conquering state in Italy, even if the goal was to take Italy
back. Foreign troops did get sent there. Of course, locals would also have joined to fight the Germans, and later the Saracens, as well as serving in the local militia.
Basically, it was different from the Classical Era when the city states, although settled from Greece, were independent and made decisions in their own self-interest. Belisarius and the highest civilian rulers were making decisions based on the good of the Empire as a whole, not the good of southern Italy. Taxation was ruinous, the administration not always good. Then, while I'm pretty sure the sentiment was, better to be part of the Empire than under the Lombards, The Gothic War devastated Italy more than the Germanic invasions...lots of taxation, lots of devastation, lots of carnage, and then left to the Langobardi and the Saracens.
As to how people identified, I think it probably varied by area. In Liguria, only recaptured for a short time, and never Greek speaking, I think the identification was probably pretty shallow. In southern Italy where it lasted for along time and there were lot of Greek speakers, I' m sure it was deeper.
As to how close the people of Puglia and Calabria of that time (pre-and post Gothic War) were, genetically, to the people or Greece , I don't know. We need a dna.