[3.13] gh-126664: revert: Use else instead of finally in docs explaining "with" (GH-128169) (#128170)

gh-126664: revert: Use `else` instead of `finally` in docs explaining "with" (GH-128169)

Revert "gh-126664: Use `else` instead of `finally` in "The with statement" documentation. (GH-126665)"

This reverts commit 25257d61cf.
(cherry picked from commit 228f275737)

Co-authored-by: Gregory P. Smith <greg@krypto.org>

Doc/reference/compound_stmts.rst

@@ -534,15 +534,18 @@ is semantically equivalent to::
     enter = type(manager).__enter__
     exit = type(manager).__exit__
     value = enter(manager)
+    hit_except = False
 
     try:
         TARGET = value
         SUITE
     except:
+        hit_except = True
         if not exit(manager, *sys.exc_info()):
             raise
-    else:
-        exit(manager, None, None, None)
+    finally:
+        if not hit_except:
+            exit(manager, None, None, None)
 
 With more than one item, the context managers are processed as if multiple
 :keyword:`with` statements were nested::