How is investigation of Modi by "Supreme court of India" an independent investigation? It is the classic case of "we looked into our wrong doing and found nothing"
Yes, the investigation is independent. What I believe you mean to suggest is that it is not impartial and lacks the adversarial natural of a US legal tribunal.
During the first impeachment trial they agreed to not hear from any witnesses or allow new documents into evidence since his party controlled the senate.
This is just an argument about definitions. "Independent" means "from a different power center".
Now, it is entirely fair to argue that that the powers in question are colluding in some way. But most states that haven't been subverted into authoritarianism have multiple actors with the power and (sometimes) will to investigate other ones.
I mean, if you take that argument far enough, no human could judge any other human, because none of them are "independent".
“How is the investigation of US president trump by the US congress an independent investigation…?”