Brendan Perry, formerly of Dead Can Dance put out an album a couple years ago called "Songs of Disenchantment: Music from the Greek Underground " that was a bunch of old Greek folk songs. Probably not as ancient as you're looking for, but not really modern either.

Found a guy on Youtube a few years back named Peter Pringle who plays a variety of ancient music, though it mostly tends to lean Babylonian or Sumerian https://www.youtube.com/@copperleaves