I think I have four that are top of my current most played songs that aren't English:

Kaval Sviri, a Bulgarian folk song. Specifically the version performed by KSS, a women's choir in Oslo. It's a cappella, and has some great resolving dissonance. Really a fantastic performance.

Next would be Ka Bohaleng performed by Abel Selaocoe. It has some cool string effects and I like the throat singing technique he uses in this song in particular.

Presidente by Goran Bregović (featuring Gipsy Kings) is a fun upbeat celebratory song.

Altay by Ummet Ozcan, featuring vocals from Otyken is a great song that feels like... Mongolian cyberpunk? If that's a thing. If you can't tell I'm really feeling throat singing multiphonics right now 😆