Italy's approach is that the inconvenience must now fall on the unvaccinated. The Green Pass and Super Green Pass (the latter is the one showing you've had the booster) are now being required for virtually everything, including quite basic things like public transport. The option to show a negative test in lieu has been removed, and now only applies to the workplace.
If you have a Super Green Pass you can still eat in restaurants, go to bars and anything that's still open. If you haven't been vaccinated, you can't do much of anything.
I read yesterday that a McDonalds and a restaurant in our region had been closed for 5 days and fined because staff didn't ask to see someone's Green Pass - unfortunately that someone was a police officer.