Just some data points from my personal experience...
On our recent 3-week Sicily trip, Amex was accepted by all franchisees (e.g. car rental), most innkeepers and maybe a third of merchants and restaurants. For reference, we lodged mostly at smaller family-run places, ate at smaller places and did a variety of tours and museums. Oftentimes, the merchant would have to grab a separate card reader for the American Express, but I was always deferential and they were always "no problem".
It was also my first time using a Charles Schwab debit card that I had specifically set up and loaded for international travel. It was accepted at every ATM I used, but I only used bank-affiliated ATMs