Regarding the decline of the Byzantines though, well they mostly kept loosing territory after Egypt with back and forwards here and there. How is that not a decline?
Much worse can be said for the western part of Rome and for any Empire in history. I think you ought to study Byzantium a little bit more deeply. Byzantium warps time and this warping leads to misunderstandings because people move in phases and in this case centuries represent a single phase which is not true for any other state most people are familiar with.
The loss of Syria and Egypt to Islam was indeed a massive blow as these were core territories almost entirely inhabited by Greeks after 1000 years of unbroken rule there.
Nevertheless, Byzantium still produced effective military commanders, had global reach, redesigned itself a few times administratively and survived with dignity very potent enemies like the Muslims, the Golden Horde, the Slavs who were forces of nature. It managed to convert the Russians and the whole of the Slavic world consequently bringing it firmly within the bossom of the Empire, eventually expanding its influence & cultural footprint all the way to Japan.
You said earlier the Greek East was richer than the Roman West, even when you take Egypt out of the picture, the Greek East was richer because it was a lot more unified, cohesive, integrated & efficient than the western part. The western part went through an economic crisis the very moment it stopped the wars of conquest, peace was destructive to the western Roman economy without booty flowing around and peace was unsustainable for its economy. This is the kind of longevity that matters. The Greek East on the other hand resembled a modern nation-state from early on and died as a nation-state rather than as an Empire of various peoples. It maintained its cohesion & economy during peace and war alike.
Rome recognized from very early on that the Greek element is overwhelming and cohesive in the East and actively pursued policies of Hellenization for conquered territories in the east instead of policies of Romanization as in the west and north of Europe.
This is all down to Alexander.
When a state grows rich and strong, adjacent peoples start taking notice, they start copying and catching up with the strong one. Rome was tested by the Gauls on the north and fell the very moment they got sufficiently organized, she was unable to keep a sustainable border at the face of constant attacks. Byzantium on the other hand went through this test again and again and again, plenty a time and kept its core borders sustainable for an extra 1000 years against an insane amount of groups up to and including its own allies.
You can see these core borders clearly because when the Persian Sassanids were totally defeated in 628 AD, the Byzantine Emperor just demanded these core borders in a gracious status-quo ante. He just wanted what was Roman before the Persian invasion despite the fact that he was the total victor.
Funny/ironic turn of history that they would both be attacked by the newly found Islamic Arab Muslims with Persia falling in its entirety and Byzantium losing these core territories of Syria, Egypt and Cyrene but still holding modern Turkey, Armenia, Georgia and parts of Syria in the East.
https://en.wikipedia.org/wiki/Byzantine ... 2%80%93628Byzantium outlived Charlemagne's Empire which was western empire 2.0 and also outlived the German Otto's Empire which was western empire 3.0 all the while receiving tribute and honours from these copycats.
Byzantium outlived 3 separate versions of the western Roman empire by 3 separate peoples, the Romans, the Franks and the Germans.
EN EL ED EM ON
...take your common sense with you, and leave your prejudices behind...