IE Language group origins from Southern Caucuses/Armenian Highlands/Northern Iran
The language group Persian is under is listed as Indo-European with no mention it has origins in Northern Iran in its name. Should be Irano-European language group at least. It was our Iranic ancestors that gave the Proto-Aryan language to Northern India.
We know now the Yamnaya culture was not the originator of the language but inherited and eventually spread the language and with far reaching distance due to their use of wheeled technology. Yamnaya culture contained a large admixture from the Caucasian HG DNA combined with Eastern HG DNA which makes sense given the origins of the IE languages started from Southern Caucuses and they would have inherited the language through their Southern Caucasian ancestors.
Early on in the development of the language it spread west in Anatolia and would eventually form the earliest attested IE language, Hittite. And we know from genetic research Hittites did not have Yamnaya DNA. Another migration reached the Pontic-Caspian and Forest Steppe around 7000 years ago, and from there subsequent migrations spread into parts of Europe around 5000 years ago.
Caucasian Hunter Gatherer DNA is also directly related to Iranian Zagrosian Hunterer Gatherer DNA so indirectly Europeans through Yamnaya do have ancestry related to Iran through CHG DNA.
Through the Yamnaya migrations eastward the development of a new culture called the Sintashta culture (Proto-Proto-Iranic ancestors) would come to fruition and eventually through migrations south into Central Asia come FULL CIRCLE back into Iran as a more modern variety of the ancient language that was originally spoken in its northern lands.