How likely would luggages stored under buses be stolen in Sicily, Naples, or Amalfi Coast?

Personally I think the idea of luggage theft is overrated. Who wants to run off with a bag of dirty clothes? A better target is your billfold ('case we know it has cash) or perhaps your day bag that may have a cell phone, billfold, or something else that is valuable and is easier to grab. For the most part pickpockets are experience and just not going to grab any old bag. In a years travel in Europe over 40+ years we have never had a luggage problem on either buses or trains. Sometimes when on long trips we may tie the handles of our two carry on size bags together so that if one is grab the other is a surprise dead weight. Whether that works or not is probably open to question. That might prevent a grab and dash or someone accidentally grabbing the wrong bag.

However, we are very careful with the day bag but we never had any problems with the day bag because we just keep it in a location that is difficult for anyone to get to it.

Over the last 5 years we have taken intercity buses, with underbus luggage storage, several times with no problems - specifically, we have taken the bus from the Catania airport to Sirausa, and from the Catania airport into the city. If you're worried, I like the suggestion of tying 2 bags together, but that might be hard to manage physically when getting your bags into and out of the storage - typically there are a lot of people crowding around and shoving their bags in or pull theirs out.

It can happen anywhere, but does not happen frequently. There are reports on the Italian media (including social media) of bags being taken from the belly while some passengers descended at intermediate stops. The reports in particular single out the long distance Flixbus European wide trips, often occurring at night, and often refer to locations all over Europe, not only Italy, for example it could be from Rome to Marseille or Turin to Paris. Some Italians who were actually robbed that way, said that they get off the bus at each intermediate stop to observe that they don't take their bags. For local daytime travel, like your are probably taking, the phenomenon may be even rarer, however make sure you take the valuables (phones, passports etc.) with you on the overhead compartment. Another strategy could be to use a cable lock to lock multiple bags together. I use that strategy on trains (trains have overhead compartments and also larger holds and both sides of each car for larger suitcases) and even in the trunk of my car, so that I can stop at freeway rest stops or restaurants without worrying too much about people opening my trunk and grubbing my bags. Locking cases together in a buses' hold may not be possible however, as sometimes it is the bus crew (the driver) who does the loading in the hold.

We took buses across Sicily in 2023, and the bus to and from the airport in Palermo.
We made sure to sit above the luggage compartment so we could see what was being removed.
You could also get out and watch the unloading process.
Also, put AirTags in your cases.

Some buses have holds that open on both sides, so it would not always be possible to see what's going on from above.

In the last ten years I've spent over 36 months in Europe, visiting over 20 countries. I've taken intercity buses, accompanied by luggage, in many places, including Sicily. My suitcase is too large for me to lift overhead, so it always goes in the hold on a bus. On trains I leave it on the rack if space is available, where it is usually out if my eyesight. I've had no problems with theft.

From the perspective of a thief, would you risk stealing a run-of-the-mill, cheap suitcase? That's what I have, so I figure my bag is not an attractive target.