Probably ADE. Since the people dying in Italy are now fully vaccinated simply due to the vaccinated status, they do not wish to show low Vaccine Effectiveness.

This way, they can make Covid be a sudden illness only and write-off the deaths of other healthy adults to "comorbidities". This is what they did in Singapore when they realized the numbers were not looking good, they decided to stop reporting deaths by vaccine status and instead started writing general statements like "Most had multiple co-morbidities".

Given that we live in a world where virtually anyone can be labelled "co-morbid" (example: A Sumo Wrestler would be classified as morbidly obese, but they've not died in record numbers in Japan because obesity is not a marker of un-health or risk by itself), this is a very sneaky way to hide the deaths of people who were healthy and got Vaxxed out of business.

Just my theory.