Determining the number of vertices of a selected object in QGIS 3

You can use the following script in QGIS Python Editor. Select a layer, run the script and select a feature.

def n_vertices(selected, _, __):
    n = len(selected)
    
    if n == 1:
        g = iface.activeLayer().selectedFeatures()[0].geometry()
        print(len([v for v in g.vertices()]))
    elif n > 1:
        print("Select only one feature")
        
iface.activeLayer().selectionChanged.connect(n_vertices)