I didn't get what you mean, do you mean R1a-M417 is Proto-Indo-European haplogroup? So both Bronze Age Fatyanovo and Levant were Proto-Indo-European cultures in the 3rd-2nd millennium BC?!
The fact is that none of ancient samples from the 3rd-2nd millennium BC in India, Iran, Levant and other regions where Indo-Iranian lived is R1a-Z93, according to "The Formation of Human Populations in South and Central Asia", by Vaghees Narasimhan et al., Steppe ancestry reached South Asia after 1000 BC, about 600 years after the appearance of Indo-Iranian culture in the Levant.
Haplogroups don't speak languages nor practice any culture. What we can say is if a certain haplogroup or clade of haplogroup is strongly linked to a certain population or culture of antiquity and was diffused together with the expansion of the former. Of course the haplogroup remains (unless the lineages die out entirely) long after the language and the culture have changed or even have totally disappeared due to acculturation enacted by another population (e.g. Turkic arriving in medieval Anatolia, Hungarian arriving in medieval Pannonia).
You seem to have some trouble following the chronological order of things:
TMRCA R1a-M417 - 5400 YBP (earliest samples in Northeastern Europe; earliest samples of R1a as a whole date to the Mesolithic
alsster in Northeastern Europe)
PIE language - spoken roughly between 5000 and 6500 YBP (major expansion between 5400-4600 YBP linked to spread of steppe ancestry)
CWC - 4900-4300 YBP - population of mostly steppe ancestry + some EEF
Fatyanonovo-Balanovo - eastern offshoot of CWC, 4900-4000 YBP - population of mostly CWC-like background and lots of R1a-M417 and especially Z93
Sintashta - >4200 YBP - population still mostly of steppe ancestry + some EEF and closely related to CWC
PIE changed over time and became hundreds of different languages. The culture of people speaking it diverged as much or even more so, because of admixture with others and isolation from each other. The haplogroups, though, remained the same, only developing new subclades.
What's so hard to understand, really?
The fact is that none of ancient samples from the 3rd-2nd millennium BC in India, Iran, Levant and other regions where Indo-Iranian lived is R1a-Z93, according to "The Formation of Human Populations in South and Central Asia", by Vaghees Narasimhan et al., Steppe ancestry reached South Asia after 1000 BC, about 600 years after the appearance of Indo-Iranian culture in the Levant.
Indo-Iranians lived mostly in Central Asia until the mid 2nd millennium B.C., and they may have established in at least some parts of Iran only in the 1st millennium B.C., so it's not surprising you won't find a lot of R1a-Z93 there in the 3rd-2nd millennium B.C., particularly when we know there is an almost unforgivable paucity of aDNA samples from the BA and IA Iran and South Asia until now.
Also, you need to decide what you really believe. First you say R1a-M417 and R1a-Z93 particularly are linked to Indo-Iranian peoples from Poland (sic) to India, then you now say "none of ancient samples from the 3rd-2nd millennium BC in India, Iran, Levant and other regions where Indo-Iranian lived is R1a-Z93". Contradictory statements, don't you think so?
The fact Narasimhan found steppe ancestry only in samples dating to after 1000 B.C., among very few samples from South Asia that he got, is honestly too little for us to claim confidently that there wasn't R1a nor steppe ancestry in South Asia before 1000 B.C. It's a very large and already then very populous place, and steppe ancestry must've been initially much more localized than it is now.
The Levantine samples from MBA clearly had links with a population movement of Central Asian origins, totally coherent with the way most scientists now assume that PIE and steppe ancestry arrived there: Eastern Europe > North-Central Asia > South-Central Asia > Iran/Transcaucasia > Levant.