DOC: Add MultiIndex.factorize extension dtype fix to whatsnew v3.0.0

Author: davidjcastrejon

doc/source/whatsnew/v3.0.0.rst

@@ -1094,6 +1094,7 @@ MultiIndex
 - Bug in :meth:`MultiIndex.from_tuples` causing wrong output with input of type tuples having NaN values (:issue:`60695`, :issue:`60988`)
 - Bug in :meth:`DataFrame.__setitem__` where column alignment logic would reindex the assigned value with an empty index, incorrectly setting all values to ``NaN``.(:issue:`61841`)
 - Bug in :meth:`DataFrame.reindex` and :meth:`Series.reindex` where reindexing :class:`Index` to a :class:`MultiIndex` would incorrectly set all values to ``NaN``.(:issue:`60923`)
+- Bug in :meth:`MultiIndex.factorize` losing extension dtypes and converting them to base dtypes (:issue:`62337`)
 
 I/O
 ^^^