[3.13] gh-119287: clarify doc on BaseExceptionGroup.derive and link to it from contextlib.suppress (GH-119657)

Doc/library/contextlib.rst

@@ -314,7 +314,9 @@ Functions and classes provided:
 
    If the code within the :keyword:`!with` block raises a
    :exc:`BaseExceptionGroup`, suppressed exceptions are removed from the
-   group.  If any exceptions in the group are not suppressed, a group containing them is re-raised.
+   group.  Any exceptions of the group which are not suppressed are re-raised in
+   a new group which is created using the original group's :meth:`~BaseExceptionGroup.derive`
+   method.
 
    .. versionadded:: 3.4
 

Doc/library/exceptions.rst

@@ -989,7 +989,8 @@ their subgroups based on the types of the contained exceptions.
       Returns an exception group with the same :attr:`message`, but which
       wraps the exceptions in ``excs``.
 
-      This method is used by :meth:`subgroup` and :meth:`split`. A
+      This method is used by :meth:`subgroup` and :meth:`split`, which
+      are used in various contexts to break up an exception group. A
       subclass needs to override it in order to make :meth:`subgroup`
       and :meth:`split` return instances of the subclass rather
       than :exc:`ExceptionGroup`.