Hello Dee and welcome to our community! There is no longer a domestic green pass requirement in Italy. The only time you'll need to show a basic green pass is for entry into the country, currently in place through May 31.

There is still a mandatory mask mandate for train travel. Through June 15, passengers on public transport (trains, planes, ferries, and local transport such as buses, subways, trams) are required to wear an FFP2 (N95) mask.

Here are the requirements for entry into Italy, from the health ministry webpage:

The rules for entry into Italy have been updated and simplified. The Minister of Health, Roberto Speranza, has signed a new order extending the provisions for arrivals from foreign countries to 31 May. The only change concerns the Passenger Locator Form, which from 1 May will no longer be necessary.
From 1 May, regardless of the country of entry into Italy, the traveller will be required to present to the carrier and to whoever is in charge of checking:
the COVID-19 Green Certificate or other equivalent certificate which must state one of the following conditions:
completion of the primary vaccination series or booster dose according to the vaccination plans of the countries of release with vaccines authorized by the European Medical Agency (primary series validity 9 months and booster dose without predefined limit)
recovery from SARS-CoV-2 infection (valid for 180 days from positive swab test)
recovery after the administration of the first dose of vaccine or at the end of the primary vaccination series or following the administration of the relevant booster dose
rapid antigen or molecular swab test, respectively within 48 or 72 hours before entry into Italy.

Have a wonderful time in Italy!

I know Covid tests aren’t required now for train travel, but what about vaccine cards or green cards? Are they required?