BUG: get_indexer_non_unique() does not handle targets of dtype='object' with NaNs correctly

[johannes-mueller]

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the master branch of pandas.

Reproducible Example

import pandas as pd
import numpy as np

idx = pd.Index([1.0, 2.0])
target = pd.Index([1, np.nan], dtype='object')

print(idx.get_indexer(target))
print(idx.get_indexer_non_unique(target))

Issue Description

The script outputs

[ 0 -1]
(array([0, 0, 1]), array([], dtype=int64))

It boils down to the fact that in object arrays with NaNs in them the are not sorted in as expected as discussed in numpy/numpy#15499.

This is one aspect of #44465 which needs to be split due to two different root causes.

Expected Behavior

Expected output

[ 0 -1]
(array([ 0, -1]), array([1]))

Installed Versions

INSTALLED VERSIONS ------------------ commit : 700be61 python : 3.8.12.final.0 python-bits : 64 OS : Linux OS-release : 5.4.0-90-lowlatency Version : #101-Ubuntu SMP PREEMPT Fri Oct 15 20:57:56 UTC 2021 machine : x86_64 processor : x86_64 byteorder : little LC_ALL : None LANG : de_DE.UTF-8 LOCALE : de_DE.UTF-8

pandas : 1.4.0.dev0+1132.g700be617eb
numpy : 1.21.4
pytz : 2021.3
dateutil : 2.8.2
pip : 21.3.1
setuptools : 58.5.3
Cython : 0.29.24
pytest : 6.2.5
hypothesis : 6.24.2
sphinx : 4.2.0
blosc : None
feather : None
xlsxwriter : 3.0.2
lxml.etree : 4.6.4
html5lib : 1.1
pymysql : None
psycopg2 : None
jinja2 : 3.0.3
IPython : 7.23.1
pandas_datareader: None
bs4 : 4.10.0
bottleneck : 1.3.2
fsspec : 2021.11.0
fastparquet : 0.7.1
gcsfs : 2021.11.0
matplotlib : 3.4.3
numexpr : 2.7.3
odfpy : None
openpyxl : 3.0.9
pandas_gbq : None
pyarrow : 6.0.0
pyxlsb : None
s3fs : 2021.11.0
scipy : 1.7.2
sqlalchemy : 1.4.26
tables : 3.6.1
tabulate : 0.8.9
xarray : 0.18.2
xlrd : 2.0.1
xlwt : 1.3.0
numba : 0.53.1