Presently unknown.

It would not make sense for aetherytes to be in ancestral Garlean lands, but one must remember that their holdings were rather miniscule just a century ago. It would then fall on the native peoples to their conquered lands to have installed aetherytes, and seeing as the Xaela were capable of getting aetherytes in some of their more permanent settlements, it doesn't seem particularly difficult (though if we're to believe Lolorito it's somewhat costly to install and maintain).

Would the Garleans install aetherytes themselves? Maybe, maybe not. It's very useful for their conscripted soldiers, but presents a grave security risk and they can't use them themselves... they might not destroy functional ones, but I don't see them installing new ones.