Folks, here's an update to my post.
I raised a closure request via email to their Level 1 customer care on 17th October, which was replied to on 24th October night (after whopping 7 days), and they mentioned that they have taken a cancelation request.
The next day, on 25th October morning (in less than 12 hours), received the following SMS:
"Dear Customer, your IndusInd Bank Credit Card ending 0420 has been cancelled as on 25/10/2024 - IndusInd Bank."
That's it. No calls prior to it or even a confirmation email afterwards with further information.
Moreover, the card is still being reflected in the netbanking, which is weird. However, when I'm trying to change transaction preferences (POS/Online/ATM), it is throwing an error, meaning the card is not operational anymore. Will have to see when they update on CIBIL.