TST: catch exception for div/truediv operations between Timedelta and pd.NA (#58188)

* *TST 54315 Add tests for pd.Timedelta and pd.NA div / truediv

* Add release doc for TST 54315

* Apply pre commit correction for TST 54315

* "Correct bug fix description removed"

* Remove unnecessary unit test description

Author: droussea2001

pandas/tests/scalar/timedelta/test_timedelta.py

@@ -11,6 +11,7 @@
 import pytest
 
 from pandas._libs import lib
+from pandas._libs.missing import NA
 from pandas._libs.tslibs import (
     NaT,
     iNaT,
@@ -138,6 +139,19 @@ def test_truediv_numeric(self, td):
         assert res._value == td._value / 2
         assert res._creso == td._creso
 
+    def test_truediv_na_type_not_supported(self, td):
+        msg_td_floordiv_na = (
+            r"unsupported operand type\(s\) for /: 'Timedelta' and 'NAType'"
+        )
+        with pytest.raises(TypeError, match=msg_td_floordiv_na):
+            td / NA
+
+        msg_na_floordiv_td = (
+            r"unsupported operand type\(s\) for /: 'NAType' and 'Timedelta'"
+        )
+        with pytest.raises(TypeError, match=msg_na_floordiv_td):
+            NA / td
+
     def test_floordiv_timedeltalike(self, td):
         assert td // td == 1
         assert (2.5 * td) // td == 2
@@ -182,6 +196,19 @@ def test_floordiv_numeric(self, td):
         assert res._value == td._value // 2
         assert res._creso == td._creso
 
+    def test_floordiv_na_type_not_supported(self, td):
+        msg_td_floordiv_na = (
+            r"unsupported operand type\(s\) for //: 'Timedelta' and 'NAType'"
+        )
+        with pytest.raises(TypeError, match=msg_td_floordiv_na):
+            td // NA
+
+        msg_na_floordiv_td = (
+            r"unsupported operand type\(s\) for //: 'NAType' and 'Timedelta'"
+        )
+        with pytest.raises(TypeError, match=msg_na_floordiv_td):
+            NA // td
+
     def test_addsub_mismatched_reso(self, td):
         # need to cast to since td is out of bounds for ns, so
         #  so we would raise OverflowError without casting