Add strict_na keyword to the assert_.._equal methods for object dtype to help with deprecation

[jorisvandenbossche]

Adding a strict_na=False option to our assert functions (the default of True keeps the new behaviour enforced on main). This keyword is only relevant for object dtype (or when using that code path when specifying check_dtype=False and having different dtypes).

This was brought up in the original PR, see #52081 (comment), and also discussed in the original issue (#18463)

This obviously needs some more docstring and test updates, but first wanted to see how this is received

• 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.

[jbrockmendel]

Is the idea to keep this forever or just a lengthened deprecation cycle?

could be modestly be more strict by disallowing egregiously mismatched cases e.g. np.dt64(nat) vs np.td64(nat)?

[jorisvandenbossche]

or just a lengthened deprecation cycle?

No, it's actually just to make it easier to use, because for certain use cases the previous behaviour was a lot more convenient (so the title "help with deprecation" is a bit wrong, it's not to help with the deprecation process itself, but just to help live with the new enforced behaviour).

[jorisvandenbossche]

could be modestly be more strict by disallowing egregiously mismatched cases e.g. np.dt64(nat) vs np.td64(nat)?

That again would then make the keyword logic and implementation more complex. So unless there is a use case for this, I personally wouldn't do that.
(in the end, the keyword that I am adding in this PR needs to be explicitly enabled, so the user of this typically knows why they are specifying it)

[WillAyd]

What is the envisioned scope of this keyword? Does it treat None, pd.NA, pa.null and np.nan all the same? Or just a subset of those?

[jorisvandenbossche]

It will treat anything that pd.isna(..) considers as missing (for scalar input) as equal.
(so not a subset, as all those scalars can occur in an object-dtype column)

[github-actions]

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