The post office knows who you are sending letters to. They have to know because they have to deliver it. They do not know the content of the letter. They also dont know if the letter will be passed along by the receiver to a different destination.
Your ISP knows you are sending traffic to a VPN but not where they are sending it to. The VPN knows where you are sending traffic to but not the content of that traffic. So if you browse a website that only serves pirated content, then they knows you are consuming pirated media but not which media.
If the law requires the VPN to report any and all traffic to blacklisted sights then a "no logs policy" would breach that law.
However to make this law work, Italy would have to ban all VPNs and http proxy services outside of Italy. Italy would have to force pretty mutch the whole world to follow this law for it to work.
What happens if you run a tiny server on AWS in the USA to proxy your private traffic. Unless AWS USA is watching all traffic to see if it complies with Italian law there is no way to enforce it.