There's also not enough mentions made of the fact that after the reign of Manuel I Komnenos the "elites" of the empire (including its intellectuals) had started to become more and more "latinised"/Westernised, in fact I would say that 1204 happened because said elites had already succumbed to the pull of the "West" (the fact that Byzantium didn't have a proper fleet by that point is a very good indication of that, of the empire just succumbing to the West via the Genoese and the Venetians).
From that point on the real "Greekness"/the real Byzantium spirit escaped to and managed to survive at monastic institutions like Mount Athos, with Gregory Palamas and the associated hesychasm being the best example for that. But because today's history is written mostly from an Western perspective, the focus is more on people like Bessarion and Demetrios Chalkokondyles, humanists that "demonstrate" that Byzantium wasn't just a backwater barbarian place, but a real precursor to the Western Renaissance. It does not matter that Bessarion was basically a traitor to the Christian Orthodox faith and to Greekness as a whole at Florence in 1439, what it does matter is to gain "institutional" points today by making said period of history relevant to Western audiences.
And that's why the history of hesychasm is almost totally ignored in much of the Western world, and that's why Ukrainian monks like Paisius Velichkovsky [1] "bringing" hesychasm to Russian lands in the late 1700s might as well be science-fiction for said Western audiences, they don't know anything about any of that. That's why it's easier for today's Western-influenced historians to write down stuff like:
> or that Putin lays claim to Byzantium and its history.
as that would be a thing that Putin had done after a millennium of no cultural and religious active contacts between Moscow and the Greek lands.
Without hesychasm you don't have Paisius Velichkovsky, you don't have staretsdom, you don't have Dostoevsky, you don't have much of the Russian culture of the late 19th century going to today, so saying that there's nothing connecting Byzantium to modern Russia would be a big lie.