Basileia Rhomaion began as one of many 'historical reenactments' in the forms of colonies. Created by a group of wealthy people (mostly from Greece, but there were also many from Russia and several other countries, connected with bonds of the Eastern Orthodoxy faith) fascinated with the Byzantine Empire. It existed like that for many years, slowly growing stronger and losing the 'historical reenactment' trait - as in most cases of such cultures, the part about pretending got dropped in second or third generation, as the descendants of the founders genuinely obeyed the tenets of the culture they were born into.
When the Unification Wars started, the whole sector quickly fell into chaos as local Federation Navy headquarters were orbital bombarded by a democratic corsairs fleet. Some of the surviving ships ended up defecting to the Byzantine Empire, due to its leadership investing a lot into orbital infrastructure that could sustain them... and build more warships.
The Empire won the contest for being the first country to start producing military ships of at least some level of combat ability, even without access to any pre-Unification War Federation shipyards, since none of them were in the sector. What's more, the Empire had no moral qualms about ensuring its own safety by a preventative attacks, annexing several nearby planets after the chaos started.
It was mostly overlooked due to several genocidal regimes rising up in the sector. With the more centrist governments finding themselves being heavily outnumbered in face of several groups of insane maniacs (including one group that was downright omnicidal), the only power capable of standing up to those threat were the Basileia Rhomaion. Surviving democracies and monarchies (plus more tamed of the dictatorships) quite quickly banded up behind it, ultimately ending up annexed though in peaceful way. Most of those countries retained the privileges received from the emperors during their annexiation proccess, being culturally different (and having some degree of autonomy) to this day.
The enemies of Empire that it conquered during the Unification Wars had less luck. Now they form the majority of the mainline byzantine provinces. They were defeated, and their inhabitants mindsculpted into byzantines, with last of them falling before the Unification Wars period ended.
The only difference was the Thanatocracy
, said omnicidal maniacs, who were (due to reasons the Empire never announced) wiped out ot the last. With their coreworlds practically sterilized by orbital bombardment. Ever since that, the Basileia Rhomaion continues ruling over the entire sector, remaining one of the main powers of the Res Publica Christiana