i would say it's much more complicated than that. yeltsin himself was already making anti-western moves or alternatively i'd say he was making moves for the oligarchs. for example, yeltsin did everything to prevent an azeri-europe pipeline, he didn't settle for 10% of the cut chechens offered because of transit. he decided to bomb them to shit instead, which wahhabists made easy because they had bones to pick with surrounding caucasians and russian population. kosovo itself was also important but with an asterisk. russia pretty much worked against yugoslavia for the entire decade. russia and america were leading discussions about how to fix the mess in kosovo. russian minister primakov was flying to washington when americans started the bombing, which was probably on purpose and a middle finger to russia, as that meant us didn't give a flying fuck about anyone, not un, not russia. russians got very angry and primakov never came to washington, the plane came back. russia and china didn't approve of the bombing, but there's also no reason to believe you would support what milosevic was doing anyways, you sought a diplomatic and more normal solution, longer negotiations. yeltsin was very inactive about the mess still, so the military or the intelligence, not sure who thought what, sent paratroopers to slatina and almost clashed with nato. not sure out of which reasons, perhaps out of historic friendship, perhaps because they felt insulted, perhaps because nato was leading an actual open war in europe, but that was it. i would also say that the russian state kind of welcomed the whole breach of territorial integrity after that, it opened a pandora's box. in 2008 kosovo was recognised, and georgia was also attacked. crimea was taken in 2014 and two republics were made in ukraine. less cocky moves would have been made if kosovo wasn't recognised by the west. kosovo isn't recognised by russia but they saw it and decided to act.
Serbia