This brings back a memory of my solo visit to a fairly small town, Sulmona in the Abruzzi. I took the train there from Rome for a day. This was in the 1980s, so things have probably changed quite a lot since then, but it was a very traditional town that observed, for example, the evening passeggiata. At lunch time when I stepped into a restaurant, I saw that I was the only female customer in the place. The tables were all occupied by working men having their lunches. They looked kind of shocked and even embarrassed to see a woman!
The head waiter ran and got a female worker from the kitchen, and she guided me to a table. I was treated with great courtesy, but it sure felt weird -- as if I'd been transported into a men's private club!
I honestly don't remember portion size being a problem on any of my numerous solo travels in Italy, maybe because I'd usually just order a salad and a starter pasta dish or something. [[edited -- I understand (in decades past) culturally it's a no-no to ask for a doggie bag (post-pandemic I see they are fine); one European told me the restaurants feed the leftovers to pigs, but I have no knowledge of whether that's accurate.]]