BUG: td64 * masked_dtype raising

doc/source/whatsnew/v3.0.0.rst

@@ -1016,6 +1016,7 @@ Timedelta
 - Bug in :class:`Timedelta` constructor failing to raise when passed an invalid keyword (:issue:`53801`)
 - Bug in :meth:`DataFrame.cumsum` which was raising ``IndexError`` if dtype is ``timedelta64[ns]`` (:issue:`57956`)
 - Bug in multiplication operations with ``timedelta64`` dtype failing to raise ``TypeError`` when multiplying by ``bool`` objects or dtypes (:issue:`58054`)
+- Bug in multiplication operations with ``timedelta64`` dtype incorrectly raising when multiplying by numpy-nullable dtypes or pyarrow integer dtypes (:issue:`58054`)
 
 Timezones
 ^^^^^^^^^

pandas/core/arrays/timedeltas.py

@@ -51,7 +51,11 @@
     is_string_dtype,
     pandas_dtype,
 )
-from pandas.core.dtypes.dtypes import ExtensionDtype
+from pandas.core.dtypes.dtypes import (
+    ArrowDtype,
+    BaseMaskedDtype,
+    ExtensionDtype,
+)
 from pandas.core.dtypes.missing import isna
 
 from pandas.core import (
@@ -501,6 +505,10 @@ def __mul__(self, other) -> Self:
                 f"Cannot multiply '{self.dtype}' by bool, explicitly cast to "
                 "integers instead"
             )
+        if isinstance(other.dtype, (ArrowDtype, BaseMaskedDtype)):
+            # GH#58054
+            return NotImplemented
+
         if len(other) != len(self) and not lib.is_np_dtype(other.dtype, "m"):
             # Exclude timedelta64 here so we correctly raise TypeError
             #  for that instead of ValueError

pandas/tests/arithmetic/test_timedelta64.py

@@ -1602,6 +1602,31 @@ def test_td64arr_mul_bool_raises(self, dtype, box_with_array):
         with pytest.raises(TypeError, match=msg2):
             other * obj
 
+    @pytest.mark.parametrize(
+        "dtype",
+        [
+            "Int64",
+            "Float64",
+            pytest.param("int64[pyarrow]", marks=td.skip_if_no("pyarrow")),
+        ],
+    )
+    def test_td64arr_mul_masked(self, dtype, box_with_array):
+        ser = Series(np.arange(5) * timedelta(hours=1))
+        obj = tm.box_expected(ser, box_with_array)
+
+        other = Series(np.arange(5), dtype=dtype)
+        other = tm.box_expected(other, box_with_array)
+
+        expected = Series([Timedelta(hours=n**2) for n in range(5)])
+        expected = tm.box_expected(expected, box_with_array)
+        if dtype == "int64[pyarrow]":
+            expected = expected.astype("duration[ns][pyarrow]")
+
+        result = obj * other
+        tm.assert_equal(result, expected)
+        result = other * obj
+        tm.assert_equal(result, expected)
+
     # ------------------------------------------------------------------
     # __div__, __rdiv__