Thanks for all your advice and insights earlier! I ended up requesting a closure for the SBI Cashback card, and they processed it without even a confirmation call. I only received a closure confirmation via message in about a week.
A few days later, I regretted the decision and reached out to SBI via mail to check if reopening the card was possible. Unfortunately, they said it wasn't.
I tried calling their support to see if reissuing was possible, but they confirmed it couldn't be reopened. So, I decided to apply for the card again just to see what would happen—and to my surprise, it was approved in just 10 minutes! My credit limit was increased from ₹1.18L to ₹1.6L. This time, I opted for Mastercard instead of Visa.
To avoid overspending, I've set a personal limit of ₹10,000 per month on the card and removed it from Tap & Pay. As for the annual fee, I plan to deal with it for now but will try spamming them every month to get it converted to a lifetime free card.
Edit: Closed new mastercard aswell 😛😅. Yes you heard right.