BUG: Index.union with timestamp[s][pyarrow]

doc/source/whatsnew/v3.0.0.rst

@@ -879,6 +879,7 @@ Datetimelike
 - Bug in :meth:`DatetimeIndex.is_year_start` and :meth:`DatetimeIndex.is_quarter_start` does not raise on Custom business days frequencies bigger then "1C" (:issue:`58664`)
 - Bug in :meth:`DatetimeIndex.is_year_start` and :meth:`DatetimeIndex.is_quarter_start` returning ``False`` on double-digit frequencies (:issue:`58523`)
 - Bug in :meth:`DatetimeIndex.union` and :meth:`DatetimeIndex.intersection` when ``unit`` was non-nanosecond (:issue:`59036`)
+- Bug in :meth:`Index.union` with a ``pyarrow`` timestamp dtype incorrectly returning ``object`` dtype (:issue:`58421`)
 - Bug in :meth:`Series.dt.microsecond` producing incorrect results for pyarrow backed :class:`Series`. (:issue:`59154`)
 - Bug in :meth:`to_datetime` not respecting dayfirst if an uncommon date string was passed. (:issue:`58859`)
 - Bug in :meth:`to_datetime` on float array with missing values throwing ``FloatingPointError`` (:issue:`58419`)

pandas/core/indexes/base.py

@@ -5042,9 +5042,13 @@ def _get_join_target(self) -> np.ndarray:
         if isinstance(self._values, BaseMaskedArray):
             # This is only used if our array is monotonic, so no NAs present
             return self._values._data
-        elif isinstance(self._values, ArrowExtensionArray):
+        elif (
+            isinstance(self._values, ArrowExtensionArray)
+            and self.dtype.kind not in "mM"
+        ):
             # This is only used if our array is monotonic, so no missing values
             # present
+            # "mM" cases will go through _get_engine_target and cast to i8
             return self._values.to_numpy()
 
         # TODO: exclude ABCRangeIndex case here as it copies

pandas/tests/indexes/test_setops.py

@@ -10,6 +10,7 @@
 import pytest
 
 from pandas._libs import lib
+import pandas.util._test_decorators as td
 
 from pandas.core.dtypes.cast import find_common_type
 
@@ -973,3 +974,13 @@ def test_union_string_array(self, any_string_dtype):
         result = idx1.union(idx2)
         expected = Index(["a", "b"], dtype=any_string_dtype)
         tm.assert_index_equal(result, expected)
+
+    @td.skip_if_no("pyarrow")
+    def test_union_pyarrow_timestamp(self):
+        # GH#58421
+        left = Index(["2020-01-01"], dtype="timestamp[s][pyarrow]")
+        right = Index(["2020-01-02"], dtype="timestamp[s][pyarrow]")
+
+        res = left.union(right)
+        expected = Index(["2020-01-01", "2020-01-02"], dtype=left.dtype)
+        tm.assert_index_equal(res, expected)