The term I was looking for is "Johads"

https://www.notechmagazine.com/2015/06/water-johads-a-low-te...

They expressly do not dam a stream, they collect runoff. You put them in low lying areas that normally form puddles in monsoon.

The idea is to prevent runoff, just like the ones in peru.

Are there migrating fish in the area of Central India that OP talked about?

If there are fish in the river at all, the biological diversity could be limited by the inability for those fish to wander beyond their side of the dam. I am not sure if there are salmonid fish there, or other fish that require swimming upstream to reproduce. I would doubt it that far inland.

You'd be surprised. They used to go as far inland as idaho.