Apple watch series 8

While you would be able to use an Apple Watch purchased in the US with the paired iPhone, you would not be able to activate cellular on a US phone in India. There are two different models of the cellular Watch. The US/North America Region and then the European version. India would use the European version. See this support document. Apple Watch - Carriers - Apple

Also, the warranty for the US Watch is only valid in the US.

I can confirm nothing. I can tell you what I know and what Apple says. First off the carrier has to support the eSIM in the Watch. Then the model number has to match the one for your location and that is it. Given what i have been told, a US Apple Watch cannot be activated in India