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[Python] __arrow_array__ does not work for ExtensionTypes in Table.from_pandas #23334

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Description

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When someone has a custom ExtensionType defined in Python, and an array class that gets converted to that (through \_\_arrow_array\_\_), the conversion in pyarrow works with the array class, but not yet for the array stored in a pandas DataFrame.

Eg using my definition of ArrowPeriodType in pandas-dev/pandas#28371, I see:

In [15]: pd_array = pd.period_range("2012-01-01", periods=3, freq="D").array                                                                                                                                       

In [16]: pd_array                                                                                                                                                                                                  
Out[16]: 
<PeriodArray>
['2012-01-01', '2012-01-02', '2012-01-03']
Length: 3, dtype: period[D]

In [17]: pa.array(pd_array)                                                                                                                                                                                        
Out[17]: 
<pyarrow.lib.ExtensionArray object at 0x7f657cf78768>
[
  15340,
  15341,
  15342
]

In [18]: df = pd.DataFrame({'periods': pd_array})                                                                                                                                                                  

In [19]: pa.table(df)                                                                                                                                                                                              
...
ArrowInvalid: ('Could not convert 2012-01-01 with type Period: did not recognize Python value type when inferring an Arrow data type', 'Conversion failed for column periods with type period[D]')

(this is working correctly for array objects whose \_\_arrow_array\_\_ is returning a built-in pyarrow Array).

Reporter: Joris Van den Bossche / @jorisvandenbossche
Assignee: Joris Van den Bossche / @jorisvandenbossche

PRs and other links:

Note: This issue was originally created as ARROW-7022. Please see the migration documentation for further details.

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