gh-83856: Honor atexit for all multiprocessing start methods (GH-114279)

Use atexit for all multiprocessing start methods to cleanup.
See the GH-114279 PR discussion and related issue for details as to why.

Lib/multiprocessing/process.py

@@ -310,11 +310,8 @@ class BaseProcess(object):
                 # _run_after_forkers() is executed
                 del old_process
             util.info('child process calling self.run()')
-            try:
-                self.run()
-                exitcode = 0
-            finally:
-                util._exit_function()
+            self.run()
+            exitcode = 0
         except SystemExit as e:
             if e.code is None:
                 exitcode = 0