The Indus Valley has always been linked to India, just as it has to Afghanistan, Iran and China.
But the Indus Valley does have a very different history.
So a river that flows 93% through Pakistan is used as the basis for the name of India, yet a river like the ganges that flows 100% through India is not used as a basis. Can you explain why?
Hinduism, yes. Buddhism, not really. Buddha was born in Nepal, he moved to India where Buddhists got persecuted. Buddhism flourished in Afghanistan and Pakistan. It did not develop in India.
The Mahyana Buddhism which is the main form of Buddhism developed in Northwest Pakistan or Afghanistan or Kashmir. This spread to China
The other type of Buddhism developed in Sri Lanka. It spread to Japan (I need to check).
Noone has heard of the Edackal Caves! All the things your historians quote are from Pakistan's or Afghanistan's history.