DEPR: Index.__and__, __or__, __xor__
- [ ] closes #xxxx (Replace xxxx with the GitHub issue number)
- [ ] [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
- [ ] 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.

LGTM. 

xref #37374 I'd be ok merging this, but am a bit new at reviewing PRs. Maybe if no one comments in the newx few hours, I'll merge it? Thanks @jbrockmendel (and happy for you to merge these straightforward PRs as well in the future @topper-123)