Alternative Congress of Vienna: What if Austria wanted to retain Carpathian frontier against Russian Empire, but with less byzantine-catholic population (that is with less Rusyns / Ukrainians) and more with roman-catholic Poles? What if tsar Alexander I Romanov was a little more Russian nationalist and wanted to "collect Greater Russian land" for "Triune Greater Russian nation" and wanted Lviv / Lvov /Lemberg more than Polish Lesser Poland (Małopolska)? In my scenario, Austrians wanted to gain some Silesian lands, so Russians gave them former Prussian lands, than is Neuschliessien (New Silesia) with Częstochowa https://en.wikipedia.org/wiki/New_Silesia
Habsburg s retain Halicz / Khalych, small city upon the Dniestr / Dnyestr river. This is historical capital of Galicia, from which than land has taken name.
Austrians has OTL incorporated lands of northern Lesser Poland during the Third Partition, but they were forced to give it back to Principality of Warsaw (Napoleon client state) in 1809. 6 years are not so much, so the Austrian administration could be restored there
By having coal from Zagłębie Dąbrowskie and crude oil from Borysław near Drohobycz / Drohobych, that Konigreich Galizien und Neuschlessien could be more prosperous, and with the capital in Cracow, not in Lemberg / Lviv / Lwów it could be more Western oriented and maybe even could develpe its own national, Lesserpolish consciousness.
Habsburgs could also add to their titulature also 'Prince of Cracow'
On the other hand, Russian Lviv would be strongly connected with the rest of Ukraine. Definitely the Muscovite-friendly party in Western Ukrainian politics would be stronger, Tsar could favorite Ortodox Ukrainians against Byzantine-catholics and Poles, and the Russian oriented party would have benefits for being royalist. Ukrainians will be also praising Tsar for incorporating Khelm / Chełm into the rest of Ukrainian lands. The drawbacks would be weaker Ukrainian culture, as the language of science and administration would be Russian, and not Ukrainian, which was supported by Austrians in the late XIX and early XX century in Galicia.
OTLRussian controlled Lviv for a couple of months in 1914-1915 https://en.wikipedia.org/wiki/Russian_occupation_of_Eastern_Galicia,_1914–15
On current map, it would look like that:
How it could affect Polish, Ukrainian, Austrian and Russian history?
How it could affect I World War?