Both of these examples are correct. 'Split' can be used as both a noun and a verb.
In the case of:
"Kosovo was a province of Yugoslavia before its split."
The use of the term "before its split" is valid as it refers to a time before Yugoslavia got 'split' (which is, as you stated, used as a noun).
Another example of this construction using a different noun might be:
"Bob was an eager runner before his illness"
(The 'illness' being the noun) or:
"Tech ltd was a part of Science co. before its dissolution"
(With 'dissolution' being a noun).
"Kosovo was a province of Yugoslavia before it split"
This is, as you noticed, a perfectly fine use of a verb.
To adapt one of my examples from above:
"Tech ltd was a part of Science co. before it dissolved"
This is another correct example, with 'dissolved' being the verb. If a noun were used there it wouldn't make sense, like this for example, which does not work:
- "Tech ltd was a part of Science co. before it dissolution"