BUG: Index.str.partition not nan-safe

[h-vetinari]

While working on #23167, I found a corner case where Index.str.partition and Index.str.rpartition break in the presence of NaNs. I do not believe this is intentional (and it's not mentioned in the docs):

>>> import pandas as pd
>>> pd.Index(['a', 'b', 'c']).str.partition(' ')  # works
MultiIndex(levels=[['a', 'b', 'c'], [''], ['']],
           labels=[[0, 1, 2], [0, 0, 0], [0, 0, 0]])
>>>
>>> pd.Index(['a', np.nan, 'c']).str.partition(' ')
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "C:\ProgramData\Miniconda3\envs\pandas-dev\lib\site-packages\pandas\core\strings.py", line 2391, in partition
    return self._wrap_result(result, expand=expand)
  File "C:\ProgramData\Miniconda3\envs\pandas-dev\lib\site-packages\pandas\core\strings.py", line 2014, in _wrap_result
    out = MultiIndex.from_tuples(result, names=name)
  File "C:\ProgramData\Miniconda3\envs\pandas-dev\lib\site-packages\pandas\core\indexes\multi.py", line 1326, in from_tuples
    arrays = list(lib.to_object_array_tuples(tuples).T)
  File "pandas/_libs/src\inference.pyx", line 1559, in pandas._libs.lib.to_object_array_tuples
TypeError: object of type 'float' has no len()

[h-vetinari]

First off, forgot to mention in the OP (now edited) that the problem appears only for Index.

The solution is also to be found there, because the failure stems from trying to create a MultiIndex from a list of tuples containing NaNs:

>>> pd.MultiIndex.from_tuples([('a', 'b', 'c'), np.nan, ('d', '', '')])
[...]
TypeError: object of type 'float' has no len()

However, it works easily when passing a tuple of NaNs

>>> pd.MultiIndex.from_tuples([('a', 'b', 'c'), (np.nan,) * 3, ('d', '', '')])
MultiIndex(levels=[['a', 'd'], ['', 'b'], ['', 'c']],
           labels=[[0, -1, 1], [1, -1, 0], [1, -1, 0]])

Opened #23578 for that.