For the actual Original Song nominees they tend to perform as written. We Don’t Talk About Bruno wasn’t nominated, it was just an exhibition ratings ploy and they tried to do some kind of remix that really sucked. I don’t think the RRR songwriters would allow them to do that with Naatu Naatu, nor would the producers want to since it’s an actual nominee.

People have already mentioned that this isn’t allowed in the Acting categories (kind of bizarrely imo? I think it should be) but every other category allows it. Trent Reznor and Atticus Ross were nominated for the scores of both Mank and Soul a couple years ago, it happens fairly often in Costumes and Makeup/Hairstyling, and sometimes producers will have two Best Picture nominees.