Is it true that you don’t have to tip in Italy? Yes, it’s true. But people are happy if you do. In sit down restaurants, one can add ten percent or so. In the touristy places, they may expect it. But, as there are so few tourists (and right now during an orange day or month, no traveling outside your city — so only very local tourist) in Italy due to the virus, I think the foreigners make sure to tip.
In a taxi, round to the nearest Euro. In a casual place, like a stand up pizza place, no tipping necessary.
Not sure about tipping the shampoo gal/guy as I haven’t been to a salon here (a bad haircut helps keep me at home, although shaving my eyebrows would work better).