BUG: `np.linalg.eigh(complex)` give wrong eigenvectors with accelerate and netlib blas

Describe the issue:

macos-arm (apple silicon M2) only, not reproducible on ubuntu-22.04,AMD-R7

call np.linalg.eigh on a hermitian complex matrix, the eigenvectors are wrong with accelerate and netlib blas, but correct with openblas.

conda create -y -n env00 -c conda-forge "libblas=*=*accelerate" numpy

conda create -y -n env01 -c conda-forge "libblas=*=*netlib" numpy

# default if no blas specified
conda create -y -n env02 -c conda-forge "libblas=*=*openblas" numpy

seems related issue: numpy/numpy#21950

Reproduce the code example:

import numpy as np
np0 = np.array([[0,1j],[-1j,0]])
EVL,EVC = np.linalg.eigh(np0)
print(EVC)
print(EVC.T.conj() @ EVC)

Error message:

# wrong (accelerate,netlib), the first EVC is correct but not normalized, the second EVC is wrong in direction
# [[-0.70710678-0.70710678j  0.70710678+1.20710678j]
#  [ 0.70710678-0.70710678j  0.5       -0.70710678j]]
# [[ 2.        +0.j  -0.5       -0.5j]
#  [-0.5       +0.5j  2.70710678+0.j ]]

# correct (openblas)
# [[-0.70710678+0.j          0.70710678+0.j        ]
#  [ 0.        -0.70710678j  0.        -0.70710678j]]
# [[1.00000000e+00+0.j 2.23711432e-17+0.j]
#  [2.23711432e-17+0.j 1.00000000e+00+0.j]]

Runtime information:

import sys, numpy
print(numpy.__version__); print(sys.version)
## same for all: env00 env01 env02
# 1.25.2
# 3.11.5 | packaged by conda-forge | (main, Aug 27 2023, 03:33:12) [Clang 15.0.7 ]

Context for the issue:

No response

Start by running the supplied np.linalg.eigh example on macOS ARM with the accelerate, netlib, and openblas environments. Use the np.linalg.eigh entry point to compare the returned eigenvectors with the reported normalized, orthogonal result. Done means the affected BLAS configurations return correct eigenvectors for this reproduction.