And also in Turkey. It (the word, if not the stew itself) arrived to the Balkans by way of the Ottomans. (And having just now clicked through to the link, it seems to have arrived to Turkey by way of the Persians).

Apparently that's kinda where the name comes from. It's named after a Serbian musician who was known as Bora Čorba, who played for a band called Riblja Čorba (fish stew).

The wikipedia article traces it to Persian, which formed it as a compound of words from different East Iranian languages. So you are on the money with Middle Eastern. From there it spread to the Balkan via Ottoman Turkish, and also from Persian to dialectal Arabic, which would explain the occurrences in Northern Africa, and maybe even Spain

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