I kind of get the same, really. The "restored Byzantium" wouldn't be the old empire in any meaningful way. Not even in name: I'm pretty sure Catherine would never allow it to be a rival imperial crown. She'd make her grandson Constantine "king of Byzantium" or something like that. The key point is that her long-term desire was to unite this Byzantium with Russia. Then it would be an empire again.

Historically, her whole plan held about as much water as a sieve. But when you start looking at it as a long-term scheme to forge a Greater Russia, it suddenly makes a lot more sense.

The Tsar would probably adopt the title of Emperor and Basileus of the Romans, on top of his other titles. The Orthodox and Christian character would be strongly emphasized and the "Third Rome" idea would probably gain new emphasis as well, which would be used especially for political propaganda both internally and externally. I bet that they would even have children born in Imperial palaces designated as "porphyrogenetos."
 
There' also another aspect the Albanians converted relative late to Islam, so there's likely a even bigger Catholic minority among them and also a lot of crypto-Catholics (they even existed to modern day, which is one of the reasons a lot of Albanians have converted to Catholism. So there's a good chance that with Austria conquering to a lot of Albanians who called themselves Muslims the day before the invasion suddenly have become Catholics.
 
Would this hypothetical Russian puppet state be called Byzantine? Looking at some sources show me the "Greek Empire" is a name thrown around.
 
There would be some expulsions and harassment of Muslims by Russian soldiers in the more remote areas and small villages, but otherwise the Russians would probably tolerate the Muslim population that remains and try to drown them out with Russian, Ukrainian, and Greek settlement in the new cities they would build up. Internal migration of Christians to the conquered areas would probably be incentivized somehow.

As for the Austrians, I'm not sure what they would do, but the low cost option also seems likely given their circumstances and the desire for reforms and for de-mobilization. Probably a population transfer agreement with the Turks and German re-settlement would be considered the most viable option. Is this anachronistic for the late 1780s?

That's how I'd imagine it happening as well. Though a planned and organized population exchange does sound a bit anachronistic; it might be a more gradual and incomplete resettlement, community by community.
 
I'd say: "Kind of". On the one hand, most people would hardly care. On the other hand, this kind of excessive butchery was seen as barbaric. In OTL, Suvurov did actually end up with his reputation tarnished. It's more of a reputation thing than a moral debate. If news of this gets out, one may expect the elite of other countries to treat it as an example of "Russian barbarism".

There may well be disgust at that sort of thing, but not, I'd think, a culture of actual humanitarian intervention - that would be decades ahead of schedule.
It depends. Interestingly, the Austrians were indeed dropping their overly zealous attitude. One the other hand, a succesfully liberate Serbia would certainly prove eager to start killing and expelling muslims. If the Austrians push south to Albania (which they ultimately would, in this scenario), except atrocities committed by the Serbian Free Corps.

I'm not sure the Serbs would make a significant difference. The closest reference point would be the behavior of revolutionary Serbia (1804-1813), and its record was mixed: several instances of massacres or abuses against Muslims, but nothing resembling an actual policy of extermination (interestingly, a few Muslim communities entered an outright alliance with the Serbian uprising, willingly cooperating with the new authorities and even fighting alongside the Serbs). I assume Austrian armies would behave along the same general pattern.
Then there's Russia. Actually not all that into butchering muslims at all, as you say. But this case was atypical. Potemkin saw this whole war as... well, almost as a crusade. It was his mission to free the Orthodox peoples from the Turkish yoke. He explicitly wanted to exterminate these "oppressors", and pretty much got underway with that in OTL. Suvurov got blamed for it, but Potemkin had overall command, and it was his plan. Let's just say that Potemkin was a genius, but also a very ruthless man. Basically, whenever his plans for a region didn't include an existing population living there any longer, he did not hesitate the start with the ethnic cleansing. And in this particular case, he also considered it a religious and nationalist mission.

I see. Interesting information, in any case.
 
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