Italy doesn’t record entry/exit for EU/EEA citizens.
Italy is member of the Schengen Area, so their rule apply first.
According to this Wikipedia page, recording the entry and exit is not required. GDPR, in particular, requires that all personal data processing are done only when they are required by a need or regulation.
If you are a EU/EEA citizen, which includes Italy, there is no need to record about your travel.
Please do not confuse this with the systematic passport control even for the EU/EEA citizens. Border Police needs to scan your passport to ensure it is not stolen and there is no arrest warrant on your name both on Local and European databases.