The eastern romans did not abolish the Roman Senate. Nothing is known about the ultimatw fate of the senate, except that pope Gregory I stating that the institution declined to almost nothing, and later pope Honorius i turning the senate building into a church.
Eastern half of the empire still continued on for 1000 more years. You forget the Roman Emperor Constantine made an entirely new capital named after himself called “Constantinople” and moved the power of the empire eastward including the power of the senate. this was partially to balance to power of the empire, partially to delegate more effectively, and also (in the regards of effective delegation) to be closer to his main rivals. The power of Rome was no longer delegated to the west, but continued to reside in the east. After the fall of the western half, the remaining eastern kingdom came to be called Basileia Romaion, or “Kingdom of the Romans” in English. Rome didn’t end just because the west fell. Rome still continued on until 1453, almost 40 years before Columbus.
@@GamingTrio-kq4co they never did it, because the term Byzantine never existed until 16th century (almost 100 years after the fall of Costantinople). So actually, they were known only as Romans and western europeans called the kingdom as Imperium Graecorum