Have pytest.raises match against exception __notes__ (#11227)

The doctest is skipped because add_note is only available in 3.11,

Closes #11223

src/_pytest/_code/code.py

@@ -704,7 +704,12 @@ class ExceptionInfo(Generic[E]):
         If it matches `True` is returned, otherwise an `AssertionError` is raised.
         """
         __tracebackhide__ = True
-        value = str(self.value)
+        value = "\n".join(
+            [
+                str(self.value),
+                *getattr(self.value, "__notes__", []),
+            ]
+        )
         msg = f"Regex pattern did not match.\n Regex: {regexp!r}\n Input: {value!r}"
         if regexp == value:
             msg += "\n Did you mean to `re.escape()` the regex?"

src/_pytest/python_api.py

@@ -843,6 +843,14 @@ def raises(  # noqa: F811
         >>> with pytest.raises(ValueError, match=r'must be \d+$'):
         ...     raise ValueError("value must be 42")
 
+    The ``match`` argument searches the formatted exception string, which includes any
+    `PEP-678 <https://peps.python.org/pep-0678/>` ``__notes__``:
+
+        >>> with pytest.raises(ValueError, match=r'had a note added'):  # doctest: +SKIP
+        ...    e = ValueError("value must be 42")
+        ...    e.add_note("had a note added")
+        ...    raise e
+
     The context manager produces an :class:`ExceptionInfo` object which can be used to inspect the
     details of the captured exception::