For most of this period Russia tried to be friendly with the US and to follow their lead in foreign policy.
They essentially prevented a UN resolution on Kosova, then jumped into Pristina Airport at the last moment.
Yes, it was the Kosovo war which started the estrangement between the US and Russia... which didn't stop Putin from offering the US immediately help after 9/11, which also received little gratitude.
Ah yes, the wonderful Balkans, where even what to name a place is fighting words. If it weren't for the fact that the Serbs would object just as vehemently to the suggestion of Dardania, (after the old 3rd-5th c. Roman province) I think it would make perfect sense. It certainly would be more substantial that arguing over whether English uses a Anglified version of the name as rendered under the conventions of applying suffixes in the Serbian or Albanian languages.