Many people often give a lot of credit to the Roman Empire on how effective it was in terms of military prowess, politics (even though it was pretty shady and corrupt many times especially during the Roman Republic era), engineering, military strategy and so on.
But this is mostly evident during the late Roman Republic era and the early-to-mid era of the Roman Empire as the there were a few instabilities in the Roman Empire that eventually made it more suspectible to entire collapse around 476CE - from less than capable leaders like Commodus, Nero and Caligula, and lots of dispute because of the massive lands that made it hard to govern by only one person until Diocletian divided the Roman Empire into 2 and later into the Tetrarchy (which also involved some internal conflict between who ruled what who was meant to be an Augustus and who was meant to be a Caesar)
The Classical Roman Empire only managed to survive for at least 400 years and at least 200 years since the Empire was divided into the East and the West, while the Eastern half of the Roman Empire managed to survive for at least a 1000 more years
(Note - Longetivity does not necessary mean that the civilisation had lots of prowess and influence. The Byzantine Empire surely managed to prosper but until the Fourth Crusade (even reading about makles me angry that such a tragedy happened because some angry people wanted to attack someone, let alone their own allies) and when the Byzantine Empire lost almost almost all of its lands in Anatolia to the Ottamans, the Byzantine Empire was much weaker than it once was)
So ironically, while the Byzantine Empire was literally surrounded by enemies, from the Arabs and the Muslims, to the Persians, the saracens and even the Normans and the Rus (until they are became their allies and the elite bodyguards of the Emperor), it was paradoxically one of the most advanced, economically robust and thriving empire with lots of trades between Europe and Asia, massive architectural achievements like the Hogia Sophia and the Theodosian Walls and so many others (which is still very odd on how the Byzantine Empire does not get that much attention on Medieval History).
(and ironically, the Byzantine Empire still gets very little attention in general population or at least in pop culture, in comparison to the classical Roman Empire)
So how did the Byzantine Empire still manage to survive despite that it was surrounded by lots of enemies and factors that would have lost its influence entirely? What was its governing structure compared to that of the Western Roman Empire? How was it governed to keep the peace among the people of different ethnic groups and different religions? How was the military trained
I'm not in a position to give a complete answer to this, which could easily fill a large book, but there are a few things to consider.
First, the Byzantine Empire was centered on Constantinople - it was the city. That's not to deny that other cities were important or to suggest that having an imperial periphery didn't matter; but due to its size, wealth, cultural significance, administrative centrality, and concentration of powerful figures, it was far and away the most important point in the Empire. Consequently, although conquering it was not sufficient in itself to destroy the Byzantine state, as its post-1204 history shows, taking Constantinople was necessary to do so. You could not land a knockout blow on the Byzantines without conquering the city. Accordingly, the fact that Constantinople's location and immensely effective fortification made it all but impossible for a pre-gunpowder enemy to conquer (and even with cannon it took a massive, concerted effort by the much more powerful Ottoman state) is very relevant to the question of why the Empire lasted as long as it did. Again and again it was able to come back from the brink, because even in extremely severe crises - I'm thinking of the combined threat of the Avars and Persians in 626 and the Arab siege at the height of their success against the Byzantines in 717-18 - Constantinople itself was able to hold out against overwhelming odds.
Second, I would point you to a book on this subreddit's reading list, which I highly recommend: Edward Luttwak's The Grand Strategy of the Byzantine Empire. As an attempt to concisely summarize its thesis, I'd offer this. The Byzantine Empire was conscious of its limitations: it could not dominate everything around it the way that Rome at the height of its power did. Accordingly, it effected a consistent approach to strategy that made the most of its strategic situation. Key features of this included a preference for avoiding decisive battle unless victory was certain (and sometimes even then), because of the difficulty in replacing Byzantine troops, because today's enemy could be tomorrow's ally, and because of the reality that even if you completely smashed one enemy, another would appear in its place. (The power of the Muslim world to the east wasn't going away any time soon, and the story of Byzantine power in the Balkans is the story of the Empire having to adjust to successive waves of migrations and attacks by people moving out of the north.) It also emphasized careful diplomacy, which could avoid conflict altogether at times and lend major advantages when conflict erupted; for instance, if a hostile power was lurking north of the border, ally with the peoples north of them. The Byzantine Empire also enjoyed a comparatively advanced and effective taxation system, wherefrom it derived revenue in sufficient quantities, and with sufficient consistency, to be reasonably assured of maintaining an effective military force. It would be misleading to suggest that some lone far-sighted emperor set these up as "rules" for the Byzantine state as consciously-designed guidelines for how to survive; but by a mix of necessity, fortune, trial-and-error, and considered insight into the best methods to address a problem, the Empire evolved certain practices and principles that allowed it to manage, both over the scale of centuries and "in the moment" of serious crises, its strategic dilemma and thereby survive for centuries.