I presume your view is in a diferent projection because your code works when the view is in EPSG:4326.  When the view projection differs from the WFS you will need to transform the bbox extent for the WFS request from view projection to EPSG:4326, then transform the features from EPSG:4326 to view projection when reading them.

    var sourceWFS = new ol.source.Vector({
        loader: function (extent, resolution, projection) {
            var extent4326 = ol.proj.transformExtent(extent, projection, 'EPSG:4326');
            var extent4326x = [extent4326[1], extent4326[0], extent4326[3], extent4326[2]];
            $.ajax('http://wms.pcn.minambiente.it/ogc?map=/ms_ogc/wfs/Bacini_idrografici.map', {
                type: 'GET',
                data: {
                    service: 'WFS',
                    version: '1.1.0',
                    request: 'GetFeature',
                    typename: 'ID.ACQUEFISICHE.BACINIIDROGRAFICI.PRINCIPALI',
                    srsname: 'EPSG:4326',
                    bbox: extent4326x.join(',') + ',EPSG:4326'
                }
            }).done(loadFeatures)
            .fail(function () {
            alert("error loading vector layer");
            });
            function loadFeatures(response) {
                var formatWFS = new ol.format.WFS();
                sourceWFS.addFeatures(formatWFS.readFeatures(response, {
                    dataProjection: 'EPSG:4326',
                    featureProjection: projection
                }));
            }
        },
        strategy: ol.loadingstrategy.bbox,
    });
    
    var vectorLayerWFS = new ol.layer.Vector({
      source: sourceWFS,
    });