I'm a huge fan of this bit of AH potential, although it should be noted that in OTL, every serious attempt failed and was doomed to fail. The timing was always off. I've repeatedly proposed that if Potemkin hadn't gotten distracted by the idea of a war with Persia in the 1780s, an Austro-Russian compact to carry this out could have come about a few years earlier.
That would have lead to a golden opportunity, because -- if successful -- Austria would immediately thereafter be distracted by the French revolution. This would allow Russia to have a pretty free hand in organising the new "Byzantine Kingdom" (note that using the term "Empire" would be diplomatically untenable; other powers wouldn't accept it).
It should also be noted that the plan went to various iterations, and the map you show only indicates one version. The ATL I have proposed here would cut Venice out of the venture, for instance, and (per Potemkin's ambitions) would go much further in attempting to dismantle the whole Ottoman Empire. Northern and Western Anatolia were to be cleared of Turks and then granted to the new Byzantine state (although Russia's direct annexations in the North would presumably extend to Cape Sinope). Armenian, Kurdish, Assyrian and Arab states were to be spun off, there was to be Austro/Russian custody of the Holy Land, and the Turks were to be confined to Central Anatolia, powerless and surrounded. Also, Potemkin´s ambitions for Romania weren´t very clear. It was also proposed that it be cut in twain, with Wallachia going to Byzantium, and Moldavia to Russia.
(Not that division would matter too much, since the Russian plan was always to have the Russian Tsars inherit the Byzantine throne, thus adding all of the new realm to Russia directly. Third Rome can into Second Rome!)
en.wikipedia.org
But it would have been absolutely epic to revive the Ruman Sultanate in central Anatolia, that's for sure! :