I know things

The correct usage in English is Roman Empire with a use of ‘east/eastern’ to give context if it’s needed. ‘During the reign of the Roman Emperor Heraclius’ ‘The 11th century tension between the east Romans and the Papacy’ ‘East Roman religious policy in the 11th century’ ‘The Roman Empire in the 7th century’ The context will determine whether you need anything other than Roman. Most of the time it will be obvious what you mean.

You’ve just expanded on your false claims instead of proving anything. It is false to say that every emperor erected a monument. It is also false to say that Phocas did. It was erected as a tribute to him by the exarch. He didn’t order its construction. There was no official language of government. Justinian issued laws in Latin and Greek with the Greeks ones coming toward the end of his reign. The idea of an official change of language is a myth. See Kaldellis’ work on this. You’ve now changed your claim from ‘the old legions disbanded’ to one single legion which was not disbanded in some great change in empire but was present during the loss of Egypt and most likely wiped out. This is far from ‘the empire ended when the legions were disbanded’ or vice versa. Heraclius did not change the form of imperial dress and he retained the title of imperative Augustus etc. Basileus was used in the east since the time of Augustus. And yes I responded to one of your claims because it was the most absurd and reveals your immense ignorance. Rome was fully part of the empire and the papacy was subordinate to the emperor. You clearly did not know the empire retook Italy and have done some emergency googling in a desperate attempt to save face. If you think that is a strawman then you are a grown man who doesn’t know what a strawman is. Your comparisons with America are a ridiculous false equivalence. If you think the relationship between America and Uzbek are anything like that of Rome and Greek you really don’t have a clue. All you have done is point to some changes that occur over the course of the long life of an empire and decided that these are tantamount to the end of a state and even with these examples you have failed. You should do more reading.