Ciao Giulia and welcome to our community! You're right, the Italian foreign ministry information is vague when it comes to talking about vaccination certificate validity. It doesn't specify the timeframe.
This is how I interpret it, however: since the foreign ministry refers to the "certificato verde" or green pass, and the regulations for validity of the green pass are in the health ministry's jurisdiction, I refer to the health ministry's regulations about the green pass. So that's six months (which could be just slightly more than 180 days depending on which months they are).