I wanted to know more about the ancestry of the Iranian population, so I found this paper from 2019.
The paper also refers to a component shared between the CIC and the Tuscans (Iran_N ??), they call it substantial in one paragraph and small in another part of the article. It is said that this component may reflect possible ancient migrations from the Near East.
A paper in which 99 percent of the authors, perhaps even more, are Iranian. Quite curious, because this is not what you often see in genetics papers. In any case, this paper seems quite outdated as methodologies, and provides not much explanation for this assumption you quoted. I looked through the whole paper, including the supp info, and nowhere I've found clear evidence of what they claim. So much so that their assumption on ancient migrations has been clearly disproved by ancient DNA: no Iran_N nor CHG, or any Near Eastern signal, has been found in the Etruscans, as claimed by the 2021 paper. Etruscans were the population of Tuscany in the Iron Age, so clearly there were no ancient or early migrations from the Near East. In 2019 some geneticists still believed the fairy tale of the eastern origin of the Etruscans. The paper does not state so but that might be the reason.
There is also a possible explanation for their assumption, the paper mentions only TSI (there are other Tuscan academic samples) and TSI is part of 1000 Genomes, a project that has a very limited sampling for Europe. For all populations of Europe there are only 4 sample sets, for Southern Europe there are only IBS (Spanish) and TSI (Tuscans), there are no Central European samples, and there are only two samples for Northern Europe GB (British) and FIN (Finnish), CEU is instead Americans from Utah (and similar to GB). It is no coincidence that a lot of the crap we have read in genetics papers in the last 15 years generally is often based on the 1000 genomes sample set. In 1000 Genomes TSI is the sample furthest southeast of Europe, so it is obvious that TSI is where potentially one may found something that can be assumed to be Iran_N and CHG. Thus, when geneticists use TSI from the 1000 Genomes project the results may be that of a very rough proxy for the Southeast European cluster than anything else.
From the chart you posted (B), it looks like they didn't use ancestral components, although they call them in this way. It may be Iran_N but but it could also be CHG, or a mix of both. Worth mentioning that the blue component, which you circled in red, which has its peak in the Baluchis, also comes out a bit to the Finns (FIN), although in a smaller percentage than in TSI. What unites Finns with the TSI-Tuscans is that they are farther east (although the Finns are clearly northern European), than British (GB) and Spaniards (IBS). The fact that that blue signal also comes out to the Finns casts a lot of doubt on the reliability of this chart, on whether it really proves anything. I'm not denying there is Iran_N and CHG in TSI but for me in the case of this study it is simply something that fills the space, just look at the PCA. If they had used samples from all southeastern European populations in the study, that blue component would have come out to them as well, and maybe even to some central-eastern and northern-eastern European populations (if it comes out to the Finns, of course it can come out to them as well).
If you look at chart C, it gets even more confusing. Here they have used samples of Europeans from other projects, and there are many more than those used in chart B. There are also samples from the HGDP project here, and so there is also another sample of Tuscans, along with Bergamo (Lombardy) and Sardinia. If you see the blue component it also comes out to others, for example a lot to Poles, and even a sample of English. In this case the study makes no observation about Tuscan HGDP. But the differences between Tuscan HGDP and TSI are minimal, not such that you can argue that one has ancestry component shared with the CIC group and the other does not. The more I read this study, the more I do not find that they have proven what they claim. If they have really found something, it is something that goes back to the Roman imperial era, but it is not something that relates specifically to the CIC/Iranian groups but to a generic genetic signal from the eastern Mediterranean.
TSI's position in a PCA.
All samples from the 1000 genomes project. 100 genomes, I think partly out of laziness and partly out of bad faith, has often been used in studies, without ancient DNA, to pull hypotheses, often even on Europeans. But given its limited sample set, it could not be the worst sample set.