I just found the below. looks like as of 1MAY like Green Pass no longer needed to use on any train in Italy. Entry conditions still have to be met min Double vaxed and no more than 9 months since last vaccination.
Effective from May 1, 2022, it is no longer mandatory to show a Green Pass to access businesses and services in Italy. Therefore, free access to local and national public transportation, bars and restaurants, shops, museums, theaters, cinemas, stadiums, gyms, spas, etc. However, a Green Pass is still mandatory to enter Italy from a foreign country.