DEPR: be stricter in assert_almost_equal

[jbrockmendel]

• closes #xxxx (Replace xxxx with the GitHub issue number)
• 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.

xref #18463 this doesn't get us all the way there since assert_index_equal and assert_numpy_array_equal go through different paths.

Note the many tests that needed to be changed; some of these likely represent undesired behaviors.

@phofl i found a usecase for downcast=False in fillna!

[mroeschke]

Do we need a whatsnew entry for this change since the testing functions are public?

[jbrockmendel]

Good idea, will update

[jbrockmendel]

updated+green

[mroeschke]

Thanks @jbrockmendel

[jorisvandenbossche]

This turns out to be a bit annoying while updating pyarrow tests for certain cases. For example, we have tests where we check that in the input you can have mixed NA-likes values. To assert the result, with this PR we need to construct the expected data with a consistent NA value. For small data it's typically straightforward to redefine it correctly. For larger data, that's a bit more annoying though.

One thing that also doesn't help is that we don't allow filling NAs with None (pyarrow uses None for object dtype arrays when converting to numpy/pandas): df.fillna(None) errors.

Should we also consider adding a keyword for relaxing this, so you can override the strict default for cases you don't care about the difference? (which was also suggested in #18463)

[CaselIT]

Any chance of getting a flag in assert_X_equal() to restore the old behaviour? It's very useful when using check_dtype=False.

Or maybe it could be connected to check_dtype (restoring the old behaviour when False)?