Fix to_excel not rendering None values in MultiIndex
- [x] closes #51252
- [ ] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [x] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [ ] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints) to new arguments/methods/functions.
- [ ] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

---

The change fixes the issue of not rendering `NaN`-valued column cells when exported to Excel.
```py
import pandas as pd
import numpy as np

Cols = pd.MultiIndex.from_tuples(
    [
        ("Item", "Type 1", "Class A"),
        ("Item", "Type 1", "Class B"),
        ("Item", "Type 2", "Class A"),
        ("Item", "Type 2", "Class B"),
        ("Item", "Type 3", None),
    ]
)

df = pd.DataFrame(np.random.randn(10, 5), columns=Cols)
df.to_excel("Test.xlsx")
df
```
<img src="https://user-images.githubusercontent.com/107754076/223540765-c4789732-eed3-4b71-aee1-8a4abfa688be.png" width="250"/>
<img src="https://user-images.githubusercontent.com/107754076/223540913-f3b11548-52de-4fcc-98aa-ddc0a666aaa3.png" width="250"/>

However, when I do roundtripping of the Excel sheet back into a `DataFrame` I get this:
```py
pd.read_excel("Test.xlsx", header=[0, 1, 2], index_col=[0])
```
<img src="https://user-images.githubusercontent.com/107754076/223541702-5a7e047f-32a6-43ed-8d3c-85b7a7ee2aad.png" width="250"/>

So I have a question. Should I update the logic of `read_excel` to also apply the conversion of `NaN` values of regular cells (specified by the `na_values` parameter) to column values as well? If so, would it make more sense to do it [here](https://github.com/GodelTech/pandas/blob/issue-51252-nan-values-multiindex/pandas/io/parsers/base_parser.py#L503-L512) (where regular values are converted), or [here](https://github.com/GodelTech/pandas/blob/issue-51252-nan-values-multiindex/pandas/io/parsers/python_parser.py#L373-L375) (where column values assigned the `Unnamed` values)? Or there's some reason why the current functionality is not applied for column values and the user is expected to convert them manually (like [here](https://stackoverflow.com/questions/40839609/rename-unnamed-multiindex-columns-in-pandas-dataframe))?

I don't believe we can differentiate between `''` and an NA value in the Excel file. Would it make more sense to assume the value is `''` instead of an NA value? Thanks for the pull request, but it appears to have gone stale. If interested in continuing, please merge in the main branch, address any review comments and/or failing tests, and we can reopen.