Fix various issues in Index.intersection

[galipremsagar]

Description

This PR fixes multiple issues with Index.intersection:

• Fixes issues with handling empty inputs, closes [BUG] Index.intersection throwing error on empty inputs #14020
• Adds validation for inputs.
• Properly handles various types in intersection implementation and fix RangeIndex.intersection by having a separate implementation for it.

Checklist

• I am familiar with the Contributing Guidelines.
• New or existing tests cover these changes.
• The documentation is up to date with these changes.

[bdice]

Some refactoring ideas.

[bdice]

@galipremsagar you mentioned this was blocking some other work -- if you'd like to move it forward and then follow up on the refactoring steps that I mentioned in comments, go ahead. I don't think those refactorings are crucial, just nice-to-have. Approving.

[galipremsagar]

@galipremsagar you mentioned this was blocking some other work -- if you'd like to move it forward and then follow up on the refactoring steps that I mentioned in comments, go ahead. I don't think those refactorings are crucial, just nice-to-have. Approving.

Addressed the refactor reviews in this PR. Thanks @bdice !

[galipremsagar]

Merging this, @bdice if you think there is more to be addressed let me know I'll tackle it in a follow-up PR.

[galipremsagar]

/merge