Austria-Hungary was a multi-ethnic empire that ruled over various Slavic populations in Central and Southeastern Europe, including the Czechs, Slovaks, Poles, and South Slavs (mainly Serbs and Croats). These Slavic peoples were often subjected to Germanization or Magyarization (the process of assimilation into Hungarian culture and language) by the Austrian and Hungarian ruling elites.
Russia, as the largest Slavic country and the main protector of Orthodox Christianity in the Balkans, felt an obligation to support the Slavic peoples of Southern Europe, especially the Orthodox Serbs, against the perceived threats from Austria-Hungary. The idea was that by supporting these Slavic peoples and helping them gain independence, Russia could enhance its prestige in the region, consolidate its position as a Slavic superpower, and gain access to the warm water ports of the Adriatic and Aegean seas.
Pan-Slavism also aligned with Russia's geopolitical ambitions in the Balkans and its ongoing rivalry with Austria-Hungary for influence in the region. Russia saw Austria-Hungary as an obstacle to its expansionist goals and viewed supporting Slavic nationalism as a way to weaken its rival.
Moreover, the Russian Orthodox Church played a significant role in fostering Pan-Slavism and promoting the idea that Russia had a religious duty to protect Orthodox Slavic communities under foreign rule. The church's influence on Russian society and foreign policy reinforced the feeling of obligation to support these Slavic people and contributed to Russia's interventionist policies in the region.
In summary, Russia felt an obligation to support the Slavic people of Southern Europe against Austria-Hungary based on ideological, political, religious, and geopolitical factors. Pan-Slavism, the desire for regional influence, the protection of Orthodox Slavic communities, and the rivalry with Austria-Hungary combined to create this commitment.