Is there a quintessential Italian hot sauce?

I have family both in the very north and the very south of Italy.

In the north, spicy food is not super common but there is usually a jar of dried chilies in olive oil somewhere in the kitchen and they are available in restaurants.

In the south there is always either fresh/dried/in-olive-oil/powdered chilies on the table (at home and in restaurants).

But I don't recall seeing a bottle of "hot sauce" anywhere (except maybe some tabasco).

Bottled hot sauce is not much in demand in Italy. I'm in central Italy, but I think in the south where spicy food is popular, chili is added fresh or dried to a dish rather than through a bottled sauce. I did find one example from Delizie di Calabria which is a common brand: http://www.deliziedicalabria.it/notizie/145-nd-sauce-la-salsa-piccante-senza-compromessi but I wouldn't call it typical. In my local supermarket (Tuscany) the only hot sauce available is Tabasco! Again, I welcome anyone from the south to correct me if I'm mistaken, but hot sauce is definitely not a thing here.

The only one I know of is the Calabrese Spread/Sauce.

Whenever I see spicy food in Italy they mostly use hot chili.

Other than that, oil flavored with spicy chili.