Drinking water in Sicily

At out hotel in Trapani there were signs to not drink water out of the taps. I believe this was because the city water was compromised by sea water.
This was a few years ago, and I don't recall a problem anywhere else.

Are you referring to house/hotel tap water? Or water on some fountains you might find in the countryside while hiking?
Water from taps in houses/hotels is safe. Water in fountains you might find in the countryside, like in a farm etc., depends.
Water in city public drinking fountains is safe unless you find a sign stating ACQUA NON POTABILE (non drinkable water).
The above is true in all regions of Italy.

I’ve just returned from Sicily.
We stayed in vacation apartments.
I always boil water when I travel, then keep it in the fridge.
I did so in Palermo, but then realised the tap water there seemed just fine as is.

In Ortigia, the water tastes salty, and was not drinkable even when boiled and cooled.
Even brushing your teeth was strange with it.
We did have to buy bottled water there.
The tap water went off completely one evening, which is apparently common there, we were told.

We purchased water while in Syracusa per Rick. Super cheap, 1.26 euro for 6 liters. We drank the water everywhere else (Catania, Taromina, Agregento, Regusa and Palermo) Have fun, don't drive;-)

This was true when we visited Trapani in 2019. I looked into it. The problem as I understood it, is that the city of Trapani's water treatment facilities do not meet current EU standards and therefore the quality cannot be assured. The hotel provided us with 2 bottles of water per person per day. According to them, the signage was required, and the city was waiting for EU money to upgrade their treatment. Apparently, still waiting.

It's like problems in Flint Michigan and Jackson Mississippi don't necessarily translate to a whole region or country. It's a local thing. Doesn't mean everywhere is bad, or good for that matter.

I don’t even drink the tap water at home in California, even though bottled water here costs 10 times what it costs in Italy. Water in Italy is safe and I use it for brushing my teeth, but many Italians don’t drink it. They either buy bottled water at the store (costs as little as 20 cents for 1,5 liters) o get special high quality purified water provided by the municipal water companies at certain municipal distribution fountains (even sparkling). In Florence such fountains are at the locations below.
https://quartieri.comune.fi.it/dalle-redazioni/riaperti-i-fontanelli-di-alta-qualita
In Palermo they are located below
https://umap.openstreetmap.fr/it/map/fontanelle-acqua-potabile-comune-di-palermo-2019_357965#12/38.1478/13.4085

We live in the Umbrian countryside, and buy water to drink. Not because we have to, but we like a little fizz in the water. We use tap water to clean and cook with otherwise. It's an aesthetic choice, not because of the water quality. That's generally true in Italy.

We drank the tap water without problem. If you don’t trust the tap water you can buy 2L bottles for about 50 cents or buy a large 5L bottle. Water is very inexpensive in stores. With a large bottle, you can refill a smaller bottle when walking around rather than continuously buying small bottles.

We lived in Sicily for four years and, on the advice of local residents, avoided consumption of tap water.