> In fact, "Balkans" in particular is an extremely ambiguous linguistic term and can mean so many different things to so many people.

Not really, Balkan countries are well-defined and have been so for over a century now. It's basically European countries that were under the Ottoman Empire:

Greece, Albania, North Macedonia, Bulgaria, Romania, Serbia, Kosovo, Montenegro, Croatia, Bosnia. One could also throw Slovenia in there but historically speaking, they have always been pretty different from other Balkan-folk.