Update documentation to reflect enhanced async debugging output

This commit updates the What's New documentation to showcase the improved
async debugging capabilities introduced in the remote debugging module
and asyncio tools. The documentation now demonstrates the enhanced output
format that provides much more detailed execution information.

The key documentation updates include:

1. Updated example output showing both "coroutine stack" and "awaiter
   chain" columns in the table format, clearly distinguishing between
   internal task execution state and external dependencies.

2. Enhanced tree output examples that include function names and complete
   file paths with line numbers, making the debugging information much
   more actionable for developers.

3. Addition of cycle detection error example showing how the tools handle
   problematic await patterns that could indicate programming issues.

The updated examples demonstrate how the enhanced debugging output
transforms from showing basic file paths to revealing detailed function
call stacks and execution context. This improvement makes it significantly
easier for developers to understand complex async execution patterns and
debug issues in production asyncio applications, especially when dealing
with nested coroutines and complex task hierarchies.

Author: pablogsal

Doc/whatsnew/3.14.rst

@@ -816,43 +816,58 @@ Executing the new tool on the running process will yield a table like this:
 
   python -m asyncio ps 12345
 
-  tid        task id              task name            coroutine chain                                    awaiter name         awaiter id
-  ---------------------------------------------------------------------------------------------------------------------------------------
-  8138752    0x564bd3d0210        Task-1                                                                                       0x0
-  8138752    0x564bd3d0410        Sundowning           _aexit -> __aexit__ -> main                        Task-1               0x564bd3d0210
-  8138752    0x564bd3d0610        TMBTE                _aexit -> __aexit__ -> main                        Task-1               0x564bd3d0210
-  8138752    0x564bd3d0810        TNDNBTG              _aexit -> __aexit__ -> album                       Sundowning           0x564bd3d0410
-  8138752    0x564bd3d0a10        Levitate             _aexit -> __aexit__ -> album                       Sundowning           0x564bd3d0410
-  8138752    0x564bd3e0550        DYWTYLM              _aexit -> __aexit__ -> album                       TMBTE                 0x564bd3d0610
-  8138752    0x564bd3e0710        Aqua Regia           _aexit -> __aexit__ -> album                       TMBTE                 0x564bd3d0610
-
-
-or:
+  tid        task id              task name            coroutine stack                                    awaiter chain                                      awaiter name    awaiter id
+  ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+  1935500    0x7fc930c18050       Task-1               TaskGroup._aexit -> TaskGroup.__aexit__ -> main                                                                       0x0
+  1935500    0x7fc930c18230       Sundowning           TaskGroup._aexit -> TaskGroup.__aexit__ -> album   TaskGroup._aexit -> TaskGroup.__aexit__ -> main    Task-1          0x7fc930c18050
+  1935500    0x7fc93173fa50       TMBTE                TaskGroup._aexit -> TaskGroup.__aexit__ -> album   TaskGroup._aexit -> TaskGroup.__aexit__ -> main    Task-1          0x7fc930c18050
+  1935500    0x7fc93173fdf0       TNDNBTG              sleep -> play                                      TaskGroup._aexit -> TaskGroup.__aexit__ -> album   Sundowning      0x7fc930c18230
+  1935500    0x7fc930d32510       Levitate             sleep -> play                                      TaskGroup._aexit -> TaskGroup.__aexit__ -> album   Sundowning      0x7fc930c18230
+  1935500    0x7fc930d32890       DYWTYLM              sleep -> play                                      TaskGroup._aexit -> TaskGroup.__aexit__ -> album   TMBTE           0x7fc93173fa50
+  1935500    0x7fc93161ec30       Aqua Regia           sleep -> play                                      TaskGroup._aexit -> TaskGroup.__aexit__ -> album   TMBTE           0x7fc93173fa50
+
+or a tree like this:
 
 .. code-block:: bash
 
   python -m asyncio pstree 12345
 
   └── (T) Task-1
-      └──  main
-          └──  __aexit__
-              └──  _aexit
+      └──  main example.py:13
+          └──  TaskGroup.__aexit__ Lib/asyncio/taskgroups.py:72
+              └──  TaskGroup._aexit Lib/asyncio/taskgroups.py:121
                   ├── (T) Sundowning
-                  │   └──  album
-                  │       └──  __aexit__
-                  │           └──  _aexit
+                  │   └──  album example.py:8
+                  │       └──  TaskGroup.__aexit__ Lib/asyncio/taskgroups.py:72
+                  │           └──  TaskGroup._aexit Lib/asyncio/taskgroups.py:121
                   │               ├── (T) TNDNBTG
+                  │               │   └──  play example.py:4
+                  │               │       └──  sleep Lib/asyncio/tasks.py:702
                   │               └── (T) Levitate
+                  │                   └──  play example.py:4
+                  │                       └──  sleep Lib/asyncio/tasks.py:702
                   └── (T) TMBTE
-                      └──  album
-                          └──  __aexit__
-                              └──  _aexit
+                      └──  album example.py:8
+                          └──  TaskGroup.__aexit__ Lib/asyncio/taskgroups.py:72
+                              └──  TaskGroup._aexit Lib/asyncio/taskgroups.py:121
                                   ├── (T) DYWTYLM
+                                  │   └──  play example.py:4
+                                  │       └──  sleep Lib/asyncio/tasks.py:702
                                   └── (T) Aqua Regia
+                                      └──  play example.py:4
+                                          └──  sleep Lib/asyncio/tasks.py:702
 
 If a cycle is detected in the async await graph (which could indicate a
 programming issue), the tool raises an error and lists the cycle paths that
-prevent tree construction.
+prevent tree construction:
+
+.. code-block:: bash
+
+  python -m asyncio pstree 12345
+
+  ERROR: await-graph contains cycles - cannot print a tree!
+
+  cycle: Task-2 → Task-3 → Task-2
 
 (Contributed by Pablo Galindo, Łukasz Langa, Yury Selivanov, and Marta
 Gomez Macias in :gh:`91048`.)