Many Indian ethnicities ruled over India as well, everything else seems to be superflous. There was never a single Chinese state that different dynasties and ethnicities in China took turns to rule over. It was one dynasty subjugating and taking land from another much like India. There was still a China just like there was still an India.
Why can't Aryavarya be a basis for modern India? Borders shift all the time. The France we see now is very different from emperor Charmanglane's kingdom.
Even then this assessment is blatantly false. The country and its people had been united, that too very recently under Mughal empire which literally coined the term "Hindustan" . Heck many practices and state systems of British India, including the "rupee" currency was derived from what came before. And that's just one example.
The place has been politically fractured many times but so have been China and others
Again, this is not about ethnicity. Saying that a country never existed before Y cuz the current state did not exist is gigacope. German and Russian ethnicities have existed for some time, but so have the ethnicities that fall under modern India. The only difference is no Indians (except Bangladeshis) have formed an ethnic nation. But that does not mean they were not Indians in the current usage of the word.
This is frankly a rather bizarre assessment of history and anthropology
Ruled over India, except that never happened, it was all fragmented and differentiated, but that wasn't the case in China. Every Chinese dynasty that succeeded another was following the rule of heaven, where they thought heaven would destroy old immoral ruling peoples. It's not just politically the same, but culturally, which is not the case of India either. There was no such concept in India that united them like they did in China.
Aryavarta can't be the basis for modern India because it specifically referred to the Aryan people of Northern India and their culture. It did not include Southern India and parts of Eastern India. Most Indian nationalists will never agree to this idea because they want control over South India, and it's all an ideological power play.
Mughals did not unite all of India, many parts of South India were not under the control of the Mughal Empire. The term Hindustan was made by foreigner Mughal rulers, and even then it mostly referred to Northern India or the entire continental landmass (not a nation), as even in music Northern Indian music is called Hindustani while South Indian Music is called Carnatic despite them evolving from the same Northern Indian music style.
The usage of rupee and other such things are due to the great influence of Northern Indian in history, as it is also commonly used to refer to money in many other places like Indonesia and Tibet. I only consider China an ancient country because it has huge historical and cultural overlap with another, and many groups claim to be inheritors of Chinese culture. No ethnic group has historically said they are inheritors of Indian culture until modern Hindutva groups came along and pushed their anti-historical narrative.
Your comparison of Russian and German nations to India is dishonest, because each ethnic group had their own nation and not a loose collection of them. India can be more likened to the whole of Europe, a continent of its own, rather than a nation. The reason that Ancient Indians have never formed their own ethnic nations is because nation is a modern concept that derives from Europe, and that's just not how Ancient India existed back then. China just coincedentally had most of those criteria of being a nation.