Description

np.vdot of a zero-length object array returned None instead of a zero-like result. OBJECT_vdot never wrote an identity value when n == 0, so the output pointer stayed NULL and PyArray_Return turned that into None.

This is the same empty-product case that np.vecdot hit in gh-31019. The fix matches gh-31033: store 0 when the contracted axis has length 0.

vdot flattens, so all of these now return the scalar 0:

>>> import numpy as np
>>> np.vdot(np.empty((0,), dtype=object), np.empty((0,), dtype=object))
0
>>> np.vdot(np.empty((1, 0), dtype=object), np.empty((1, 0), dtype=object))
0

Fixes #31735