Split, as many other English words, can be used both as a noun and as a verb.

All these sentences are fine:

There's a split down the back of your jacket.

Here's your split [=portion, share] of the proceeds.

We agreed to a fifty-fifty split of the profit. [=we agreed to divide the profits equally]

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).

Meanwhile:

"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"