the nearest point/vertex point of linestring

The point returned is the nearest point on the line to the original point. The nearest point is not necessarily an existing vertex in the LineString, and in this case it isn‘t.

end = Point(19.125150,72.893218)
np = Point(19.12493833590478, 72.89314854771877)
expected = Point(19.124929, 72.893177)

print end.distance(np) # 0.000222767386696
print end.distance(expected) # 0.000224770994572

If you want to find the nearest vertex you should first convert the LineString to a MultiPoint geometry, then use the nearest_points operation (note the minor floating point error):

from shapely.ops import nearest_points
from shapely.geometry import MultiPoint
mp = MultiPoint(route)
print nearest_points(mp, end)[0] # POINT (19.124929 72.89317699999999)

This query requires calculating the distance between the original point and each vertex in the original linestring.