[3.13] GH-79714: Add mention of stderr for clarity to ArgumentParser.exit() (GH-123932) (#124331)

GH-79714: Add mention of stderr for clarity to ArgumentParser.exit() (GH-123932)
(cherry picked from commit 5f5c0b9)

Co-authored-by: Savannah Ostrowski <[email protected]>

Author: miss-islington

Doc/library/argparse.rst

@@ -1455,7 +1455,7 @@ The ``deprecated`` keyword argument of
 specifies if the argument is deprecated and will be removed
 in the future.
 For arguments, if ``deprecated`` is ``True``, then a warning will be
-printed to standard error when the argument is used::
+printed to :data:`sys.stderr` when the argument is used::
 
    >>> import argparse
    >>> parser = argparse.ArgumentParser(prog='snake.py')
@@ -2235,8 +2235,8 @@ Exiting methods
 .. method:: ArgumentParser.exit(status=0, message=None)
 
    This method terminates the program, exiting with the specified *status*
-   and, if given, it prints a *message* before that. The user can override
-   this method to handle these steps differently::
+   and, if given, it prints a *message* to :data:`sys.stderr` before that.
+   The user can override this method to handle these steps differently::
 
     class ErrorCatchingArgumentParser(argparse.ArgumentParser):
         def exit(self, status=0, message=None):
@@ -2246,8 +2246,8 @@ Exiting methods
 
 .. method:: ArgumentParser.error(message)
 
-   This method prints a usage message including the *message* to the
-   standard error and terminates the program with a status code of 2.
+   This method prints a usage message, including the *message*, to
+   :data:`sys.stderr` and terminates the program with a status code of 2.
 
 
 Intermixed parsing