AttributeError: module 'mediapipe.python.solutions.face_mesh' has no attribute 'FACE_

Yes, FACE_CONNECTIONS is renamed to FACE_CONTOURS. Please see the new drawing example code at https://github.com/google/mediapipe/blob/master/docs/solutions/face_mesh.md#python-solution-api.

Update:

FACEMESH_CONTOURS

is the correct new name.

If you have problems with FACE_CONTOURS also try FACEMESH_CONTOURS