Anatolia_N definitely has that typical MidEast look. Its probably a MidEast look because there's so much related ancestry in MidEast.
You are making a big mistake here. How do you know what the "Middle Eastern" look was even 2000 years ago? That is like saying Loshbour had a typical European look, while even those in the Baltics have at least ~50% post mesolithic Near Eastern DNA.
The Anatolian_Neo DNA peaks in modern South Europeans, the sekeltal remains from Catal Höyuk where almost all described as Robust with long cephalic index (Dolichocephalic). The same with the Natufian and Levantine_Neo skulls.
The Iranian_Neo skulls and CHG must have been slightly less long (meso to dolichocephalic) and dinarizted, broader in going slightly into EHG direction.
CHG and Iran_Neo were so unrelated they could have been something different.
This statement isn't really correct. Yes they were different this is why I didn't put them together. Yet so unrelated? The difference would be like the difference between WHG and SHG. The only difference is that Iran_Neo has some more Basal Eurasian(~60%) than CHG (40%). But both have an ANE like component as their other ancestry, which is around 40% in Iran_Neo and almost 60% in CHG according to the paper.
If only Scythians never disappeared/asdilimated, they'd be the best EHG reference. At the moment I'd say Europeans in general, but especially Northern Europe(difference in EHG between Balt and British is slight) and maybe even Sami.
Scythian samples show ~35% EHG 35% CHG and 15% Anatolian_Neo, ~10% East Eurasian and little ASI.
Scythians would have looked like a mix of the both strongest elements in most part
EHG look must be something that is speicifc (It doesn't need to be the typical look but something specific for them) for North and East Europe. And when I think of something specific found among them than it is this what many here call the "Slavic face". They often reffer to a roundish/broad face with middle long skull (brachy or mesocephalic).
But the fact that EHG and WHG are actually today the weakest components in all of West Eurasia makes it obvious that we will have harder time finding representatives of these two than the other.
And of course naturally there will be overlap with all of them. You will see overlap between Anatolian, Levant, Iranian- Neo and CHG. As well overlap between Anatolian, Levant_Neo and WHG. While there will be overlap between CHG, Iran_Neo and EHG too.