Closed since late December, "the Green Blue Path from Vernazza to Monterosso has been restored, following the reconstruction of collapsed dry-stone walls and maintenance of the path. (Sede del Parco Nazionale delle Cinque Terre, 17 Mar 23) The stretch of the REL SVA path no. 592 from Vernazza to Monterosso has reopened, following the reconstruction of the collapsed dry-stone walls and maintenance work involving the cleaning of the ground, the restoration of vertical signs, the clearing of invasive vegetation and the regulation of water. All these activities were carried out by the Park."
For closed Cinque Terre trail information, in the Trail section of the CT Park link following, look for the trail description by number - if it doesn't say "State of practicability: Closed", it is open, though naturally, subject to change.
http://www.parks.it/parco.nazionale.cinque.terre/Eiti.php