The problem is, you defined "Roman" first using preconceived ideas and began assessing the Eastern Romans based on these ideas.

A Roman in the 1st century was primarily someone who spoke Latin, practiced Greco-Roman Paganism, and lived in Italy. A Roman in the 10th century was primarily someone who spoke Greek, practiced Orthodox Christianity, and lived in Asia Minor.

Both are unquestionably Romans. Both were recognized by their neighbors as Romans. In fact, up until the modern Greek nation state, most Greeks still identified as Roman, not Greek.

Ask an Arab, Turk, Armenian, or Persian what a Roman is, and they will describe the 10th century Roman. Ask a Western European or American, and they will describe the 1st century Roman. In truth, both are Romans, just from different time periods and geographies.

Couldn't believe how much Arabic is in Ottoman Turkish. It blew my mind when I checked out some manuscripts online. Before nationalism, Arabic, Farsi, and Turkish were syncretizing.

Sunnis in Iran were seen as a fifth column who might ally with the Ottomans should they invade Iran. The Ottomans were also putting down Shia rebellions in their own territory, and increasingly emphasizing their position as a specifically Sunni Muslim state. But because Iran was majority Sunni, brutal methods were used to quickly convert the population to Shia Islam to secure it against the Ottoman threat.