DEP: Protect some ExcelWriter attributes
- [x] closes #45572 (Replace xxxx with the Github issue number)
- [x] [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).
- [x] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

Built on top of #45794

Any attributes we're looking to make protected are deprecated here, allowing users to use them until the next major release. Not deprecating any immutable attributes - users may find these useful and they do not require any extra care.

Docs for ExcelWriter are attached.
[excel_writer.pdf](https://github.com/pandas-dev/pandas/files/7991646/excel_writer.pdf)

Thanks @rhshadrach 