With GeoNetwork, I know it’s possible to create a PostreSQL/PostGIS link with metadata.
But from to this PostGIS acess feature, is it possible to generate a thumbnail? (like for the WMS protocol)
No, it isn't possible to generate a thumbnail directly from PostgreSQL/PostGIS data in GeoNetwork (at least up to current 3.12 or 4.2 versions). You need a third party component, like GeoServer or Mapserver, to serve the data using WMS or WMTS protocols. Then you can use such service to generate the thumbnail. Another options is to use a GIS desktop client, like QGIS, to generate the thumbnail and attach it to the metadata in GeoNetwork.