Constantinople was part of the Roman Empire (as the name implies, it was 'founded' by the Roman emperor Constantine) and considered itself the Roman empire until it fell.

How was it “kinda sorta”? They were the direct, unbroken, legal and institutional continuance of the Roman Empire.

No its exactly Rome. That is what they would have called themselves and they had the provenance to back it up.

Well not exactly it was throughout Roman controlled territories throughout hundreds of years not just a single place. Often times mercenaries and raider groups. In places like the France especially. Many settlements and colonies were established and in places like north Germany it's predominately still Scandinavian. And I don't mean Denmark but Hamburg. It's where Hitler got his whole rhetoric about the superior Nordic race and the inferior slavs even though he was from Austria and Germanic not Scandinavian.