You don't need the Green Pass to enter the Cinque Terre National Park. Green Pass is only needed inside the restaurants.
On the trains you must wear a mask, the Green Pass is only required for long-distance trains. More information about Cinque Terre trains.
On Cinque Terre ferry boats you have to wear a mask, the Green Pass is only required for travellers from Versilia to Cinque Terre. More information about Cinque Terre boats.