My understanding is that it's not clear to what extent Panini understood or attempted to explicitly treat articulatory phonetics. Addressing articulatory phonetics well in writing alone is still hard, and understanding it in detail was immensely hard before the creation of audio recording, spectrograms, and x-rays.
https://en.wikipedia.org/wiki/Shiva_Sutras#Arrangement
So while a present-day understanding of classical Sanskrit grammar could be derived fairly directly from his work, that's still not any guarantee that you would pronounce Sanskrit just as Panini would have.
A moderately imperfect analogy is that while Jews have been carefully learning to read, recite, and copy the Torah for thousands of years -- including reading commentaries, which, while nowhere near as systematic or thorough as Panini, elucidate lots of grammatical issues -- there still emerged huge, systematic regional differences in the pronunciation of particular Hebrew letters, even in liturgical use.
https://en.wikipedia.org/wiki/Ashkenazi_Hebrew
https://en.wikipedia.org/wiki/Sephardi_Hebrew
https://en.wikipedia.org/wiki/Mizrahi_Hebrew
https://en.wikipedia.org/wiki/Tiberian_Hebrew
among several others. The people using each pronunciation were often incredibly sophisticated in their religious scholarship and incredibly familiar with the underlying material, but they definitely didn't (and don't) pronounce it the same way.
Modern linguistics has been able to find evidence for comparing these pronunciation variants and also understanding their histories, and I believe something similar is true for Sanskrit pronunciation.