Yugoslavia wasn't part of the EU at the time though?

You can't really judge how an alliance will respond to conflict crossing their borders on the basis of how they've responded to conflict outside their borders. Governments and militaries think borders are a pretty big deal!

More generally, there are some people in "the European project" who would like to see a United States of Europe with its own foreign policy and military. But this is pretty unpopular with voters in most member states, so everyone involved is happy to keep that level of integration on the back burner, leaving member states to respond how they like to foreign military conflicts while the EU maintains "We're a pacifist trading union, not a belligerent military alliance or a superstate, shucks we don't even have a military"

Politicians are happy to keep kicking the can down the road on EU military coordination for as long as it's politically convenient. But if an EU member state was invaded, they couldn't do that any more; they would have no chance but to make a decision.

And public opinion is far more likely to support (and may even demand) a tough, belligerent stance if Russian tanks have are invading our allies.