Baseless claim. Sanskrit is not a special ancestor to North Indian languages and there’s nothing that separates North Indian languages from southern ones. Tamil has far more influence on northern Indian languages and other Indian languages including Sanskrit than Sanskrit.
https://en.wikipedia.org/wiki/Dravidian_languages - the family that most South Indian languages belong to.
https://en.wikipedia.org/wiki/Indo-Aryan_languages - the family that most North Indian languages belong to.
In addition, there are languages spoken in India that don't fit into these categories, and are part of other families :
https://en.wikipedia.org/wiki/Munda_languages - Part of the Austroasiatic language family.
https://en.wikipedia.org/wiki/Dzongkha - Part of the Sino-Tibetan family, spoken by a sparse population in West Bengal.
None of this classification is based on "geographic" or "racial" reasons. They're classified and studied as a science.
Linguists have abounded these simplistic trees of ancestry a while back. Truth is all these languages interacted and improved one another. For example it’s likely that Dravidian languages were spoken in the Indus Valley civilization. That would make them the greatest ancestor. Sanskrit was formed much later and was likely influenced by it.
Indo Aryan itself is a racially rooted theory started by Europeans to extract familiar parts of Indian culture and define a collective identity. Reality is far more complex
The source of Sanskrit and Sanskrit influence is the Saraswat Valley civilisation around 6000 BC. Some recent books have done radio carbon, Sanskrit literature, astronomical charts, climatic events and genomics to validate the time line. The central Asian language influence is migration out of India to Central Europe & Volga referred to as Uttar Kuru.
Also what is the Saraswat Valley Civilisation? Are you referring to the Indus Valley Civilisation?
I’m sorry but the Out of India hypothesis is not accepted in the scientific and linguistic consensus in any way. The migration is believed to be in the other direction.
Also, Panini himself distinguished between different forms of Sanskrit as I understand.
Lol at your out of India theory which literally has no basis in any of what you describe
Sanskrit is used to refer to several different languages. It's often ambiguous which one people are referring to when they say Sanskrit. Classical Sanskrit is the only one which wasn't spoken as a common language.
Classical Sanskrit -- the language codified by amongst other Panini, around the 5th century BC, which was used for religious and secular purposes for high culture and amongst the political elites.
At this time, some of the other languages now called Sanskrit had turned into the "Middle Indo-Aryan languages", including Pali, and the Prakrits, whose descendents now include the modern Indo-Aryan languages of northern India, Pakistan, Bangladesh, Nepal, and Sri Lanka.
Vedic Sanskrit -- the language of the Vedas (1700BC-600BC, approximately), believed in its earliest forms to be the common languages which then became some of the modern north Indian languages. Classical Sanskrit is a codification of Vedic Sanskrit.
Broadly -- any Old Indo-Aryan language, including the pieces of Mitanni Aryan attested in inscriptions in northern Iraq/Syria/Turkey embedded in other language texts including Kikkuli's Horse training manual (mostly in Hittite, except where he uses "Mitanni Aryan" words in glosses and defines them), and king names in the Hurrian language, which are meaningful when interpreted as Sanskrit.