how much continuity was there in the dying days of rome and the beginning of what we call the medieval era?
after the barbarian invasions, the western empire transitioned through the dark ages. chroniclers visited the ruins of roman buildings and thought they must have been built by giants. christianity reemerged from places like rome (eg augustine) and ireland (eg aidan). the popes attempted to assume some level of political influence, amassing vast tracts of land and a right to tax people (peter's pence), but in the end they were thwarted by local sovereigns who weren't willing to concede temporal control of their kingdoms to the spiritual folks in rome and their local representatives in the bishoprics and monasteries. hence the investiture controversy, which was resolved by segregating different aspects of fealty/homage, and later the assertion of protestant doctrine as an alternative to roman orthodoxy.
the eastern empire, including egypt, was gradually subsumed by islam. before that, it had been in a state of schism with roman catholicism. culturally, it was more referential than original but the imperial authority was bound up in ceremonial and lacked the kind of strength required to control their own neighbourhood, let alone the world. islam emerged from the arabian desert and reduced the byzantine empire and influence to nothing. the koran has links to the biblical stories. but generally, it reflects arabian tradition, culture and language.
i don't see the controlling authority of egypt and/or rome in this narrative. or of anyone.
history has its influences. roman and egyptian ideas are two of these. and because egyptian civilisation came very early and the roman empire was very extensive, of course they have left an imprint upon the world which continues to this day. even a single institution - the papacy - which survives.
the papacy isn't rome. at its lowest ebb, the pope's empire extended little beyond the walls of the castel santangelo by the tiber in rome. the roman in roman catholicism is administratively different from the roman in roman empire. it also sought to expand, but its claim to inherit the imperial power was founded on a forgery called the donation of constantine. even so, it emerged from the dark ages as an organisation with some force and ambition in a world of chaos.
but whatever was inherited of the traditions of egypt and rome was by no means exclusive. barbarian ideas of living were some of these. there were, in the usual model of the universe, opposing forces in play. contending influences. and i like to believe that in the story of adam and eve we hearken back to a time before even egypt was born. perhaps to the hunter-gather civilisation of gobekle-tepe. (not my idea but the most romantic prehistorical speculation i have ever heard).
even if one assumes and accepts the notion that some secret roman leadership controls the world, i guess i would have to say they are doing a very poor job of it.