This quickly gets into a "Ship of Theseus" discussion. Arguable modern Turkey is the successor state to the Ottoman Empire, but would you say that modern Turkey

This quickly gets into a "Ship of Theseus" discussion. Arguable modern Turkey is the successor state to the Ottoman Empire, but would you say that modern Turkey is the same political entity as the Roman Republic? The is no objective answer to such questions - it gets down to who gets to write history and what they are trying to achieve. Charlemagne, The Holy Roman Empire and Renaissance Italy derived legitimacy by considering themselves the true successor of Rome. So did the Catholic church to some extent. Therefore western historiography have traditionally sidelined the Eastern Roman Empire. Even the name "Byzantine Empire" is part of this framing.