POC: Add the private/unused _array_dtypes function to test dtype conversions

[seisman]

Description of proposed changes

Inspired by the discussions in #3507 (comment), I think it's necessary to understand the string representation of different dtypes and what dtype they are converted to by NumPy. This PR adds a private _array_dtypes function to pygmt/clib/conversion.py. Please refer to the detailed docstrings for what the function does.

I think we should include the function in PyGMT although it's not used anywhere, similar to the array_to_datetime function which will no longer be used in PyGMT after #3507. I'm open to comments and more array-like objects should be added for testing.

[seisman]

The CI tests pass with Python 3.12 + pandas 2.2 but fail with Python 3.10 + panda 2.0:

[gw0] linux -- Python 3.10.15 /home/runner/micromamba/envs/pygmt/bin/python3.10
444     >>> _array_dtypes(np.datetime64("2021-01-01"))
445     ('datetime64[D]', 'datetime64[D]')
446 
447     For Pandas objects:
448 
449     >>> _array_dtypes(pd.Series(data=[1, 2, 3]))
450     ('int64', 'int64')
451     >>> _array_dtypes(pd.Series(data=[1.0, 2.0, 3.0]))
452     ('float64', 'float64')
453     >>> _array_dtypes(pd.Series(data=[1, 2, 3], dtype=pd.Int32Dtype()))
Expected:
    ('Int32', 'int32')
Got:
    ('Int32', 'object')

There are likely some changes between pandas 2.0 and 2.2 (or in NumPy). Anyway, it means we need to maintain the mapping from Int32 to int32 to support old versions and it also highlights the importance of this private function.