Also knowing Italy, nobody checks. Really.
I took a plane from Italy to Greece a couple of months ago: completely vaccinated and with the Passenger Locator Form ready.
Nobody, literally nobody, checked in a reliable way wheter:
- we had a valid COVID Certificate
- our PLF was filled correctly
The only moment during my trip where anyone checked was at Starbucks.
This doesn't mean that you are entitled to lie to the border control agents though.