Holy Year

I don't think anyone can really predict, but I would expect some spillover, sure.
What do you mean by southern Italy? and what month? It really depends! I can virtually guarantee the Amalfi Coast will be crowded, for example, whereas you'd have parts of Basilicata and Calabria practically to yourself.
My take is I will not be planning a trip to Rome in 2025, but I may plan one to Southern Italy or Sicily if I score a great airfare. It would not dissuade me from visiting Sicily but I have already been to the Amalfi Coast and Puglia.

Since the pandemic tourism in Italy has greatly increased. The Holy Year is going to see another increase. Yes, Rome will be very crowded. But, train travel is so easy in Italy. I honestly don't see people, even pilgrims, staying only in Rome. My gut says that Italy is going to be very crowded most of the year. That said: don't let crowds deter you! Make your plans and make reservations at hotels, museums, restaurants, trains and any flight to/from Sicily as soon as possible.

My group will be in Florence, Rome, Salerno and Taormina (Sicily) the first half of April. In Florence & Rome, I will making reservations for everything--including restaurants--in advance. For Salerno, we're doing a luncheon in Ravello on the Amalfi Coast, so we'll reserve there. But otherwise, in Salerno's Old Town--where we'll dine each night, and then in Taormina, we'll probably play it by ear, reserving day before or even same day.