If you were a Greek living in the Byzantine Empire – or as they described themselves, a Roman living in the Roman Empire – the Ottomans were just the new Roman Emperors. The Roman bureaucracy, civil institutions, and daily life changed very little.
People don't normally acknowledge it because both the Holy Roman Empire and the Russian Empire wanted to be recognised as successors to the Roman Empire, but the truth is that the Ottomans were the real successors.
Some info on Wikipedia here: https://en.wikipedia.org/wiki/Ottoman_claim_to_Roman_success...