These clusters are indeed based on moderns, but I think they do "correlate" with some ancient populations.
When you cluster people at K=3, you usually get West_Eurasian, East_Eurasian, and African clusters. at a higher K, West_Eurasian divides into a Baltic_Atlantic cluster and a Near Eastern cluster, these two ultimately divide into the four closely related clusters:
1-Southwest Asian.
2-Mediterranean.
3-North European.
4-West Asian.
4 is different from 1, 1 is high in Arabians, Levantines, and North Africans. While 4 is Caucasian, Iranian, and South_Central Asian.
When running ancient samples through calculators that employ this scheme, Iran_N and CHG score high levels of West Asian, European farmers have high Meditteranean, SHG are high in North European, and Natufians are high in Southwest Asian.
At higher K, West Asian separates into two clusters: Caucasian and Baloch/Gedrosia.
Abkhasians are a Caucasian people, they have about 50% West Asian and 25% Meditteranean, but when you have a Caucasus cluster they become 70% Caucasian, 20% Baloch, and 0% Meditteranean !! why ?
Caucasus cluster contains the Med Alleles that were previously assigned to Meditteranean, when you run ancient samples, European farmers are now 35+ Caucasian.
Look at this PCA, Abkhasians and Georgians, who are the modal populations for the Caucasus cluster, are closer to the Meditteranean than the Makrani and Baloch peoples, who are high in Gedrosia.
The reason why the Yamnaya had Baloch but not Caucasus is because they didn't have adequate EEF ancestry that would make it more Caucasian.