API / CoW: shallow copy of DataFrame/Series (.copy(deep=False)) also returns shallow copy of the index/columns

[jorisvandenbossche]

Broken off a subset of #53699, only focusing on the behaviour of df.copy(deep=False) (i.e. a "shallow copy"). And address the copy(deep=False) part of #53721.

Currently, a shallow copy of a DataFrame/Series only creates a new DataFrame/Series object, but still shares the same data (with tracking references, to ensure copy-on-write) and Index objects.
Because Index objects have some mutable aspects (not their values, but for example there name), that means that sharing an identical object in the resulting shallow copy can propagate mutations to those mutable parts of the index.

See #53721 for a longer description of the context.

This PR just updates the DataFrame/Series copy() method to also take a shallow copy of the index/columns Index object, in case of deep=False.

And based on the tests I had to update to get this passing, it illustrates some of the consequential changes in other places because of changing the shallow copy.

• Tests added and passed if fixing a bug or adding a new feature
• All code checks passed.
• Added type annotations 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.

[phofl]

lgtm

[mroeschke]

Thanks could use a whatsnew note in 2.1

[github-actions]

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[mroeschke]

Thanks @jorisvandenbossche