In answer to your actual specific question,
I am not from Italy but
I have frequently travelled to India from Europe, both short and long trips
I have never used, or taken, a credit card to India. Only debit cards.
Some thoughts,
It's incredibly unlikely you'll be renting a car there.
India is super-high-tech and mobile-oriented, so I've never had any problem using any sort of card at even smaller merchants. If you're coming from backwards Europe, or more-backwards USA, it's like stepping in to the future in terms of mobile use, connectivity etc. Think Indian programmers etc etc.
You'll surely want some cash, and the best/only way to get that is very easily at the ATMs which are everywhere.
For uber/similar (everyone uses those constantly), as I say I have only ever used/had debit cards.
At more "Western" hotels, no issue. If you stay in a more "local" hotel (where local businesspeople stay) it's possible they simply only take cash, but, if they do take cards there is no difference between debit/credit. (I've never encountered one that only takes cash, not cards.)
Some folks have pointed out that, with cards, one sometimes gets that annoyance where the company will security ping you. Unfortunately, that is true anyway if you have 1, 10, 1000 cards on you - it's just one of the nuisances of life. (If you have more cards it's almost just more annoying.) I don't see it as anything to get worked up about; there's no solution to it. It sometimes happens, annoyingly, in your own country.
Tip: if arriving in Mumbai, do not take an uber from the airport. (It's perfectly ok to take an uber/whatever to the airport, but do not take one from the airport.) Just get some local paper currency from the many ATMs on arrival, and, walk downstairs and take a totally normal yellow taxi to town. You pay (cash) at a little desk and they put you in a yellow cab (the cost is a pittance). Otherwise, use ubers/whatever freely. Or indeed, just hail a cab on the street anytime, paying the small fares with cash.
caveat India is obviously enormous, and there is nobody existing who is familiar with all cities, or even regions, of India. I know zero about many whole "universes" of India. (Maybe question should be more region specific, IDK?)
Our Lady Lakshmi will bring you a prosperous trip!

(among other things she is the patron of the welfare & education of girls; so those who follow Lakshmi you may donate, say, books to a girl's school to honor Lakshmi. subsequently whenever I flew to India I'd donate 50 or 100 bucks to say a girl's orphanage. (easy to do online!) this has made me huge piles of money in Indian business, so, it works for me - thanks only to Lakshmi. Good luck!)