Add Python SDK thread.run convenience methods (#15088)

## TL;DR
Add `thread.run(...)` / `async thread.run(...)` convenience methods to
the Python SDK for the common case.

- add `RunInput = Input | str` and `RunResult` with `final_response`,
collected `items`, and optional `usage`
- keep `thread.turn(...)` strict and lower-level for streaming,
steering, interrupting, and raw generated `Turn` access
- update Python SDK docs, quickstart examples, and tests for the sync
and async convenience flows

## Validation
- `python3 -m pytest sdk/python/tests/test_public_api_signatures.py
sdk/python/tests/test_public_api_runtime_behavior.py`
- `python3 -m pytest
sdk/python/tests/test_real_app_server_integration.py -k
'thread_run_convenience or async_thread_run_convenience'` (skipped in
this environment)

---------

Co-authored-by: Codex <noreply@openai.com>

sdk/python/README.md

@@ -19,15 +19,18 @@ installs the pinned runtime package automatically.
 ## Quickstart
 
 ```python
-from codex_app_server import Codex, TextInput
+from codex_app_server import Codex
 
 with Codex() as codex:
     thread = codex.thread_start(model="gpt-5")
-    completed_turn = thread.turn(TextInput("Say hello in one sentence.")).run()
-    print(completed_turn.status)
-    print(completed_turn.id)
+    result = thread.run("Say hello in one sentence.")
+    print(result.final_response)
+    print(len(result.items))
 ```
 
+`result.final_response` is `None` when the turn completes without a final-answer
+or phase-less assistant message item.
+
 ## Docs map
 
 - Golden path tutorial: `docs/getting-started.md`
@@ -95,4 +98,6 @@ This supports the CI release flow:
 
 - `Codex()` is eager and performs startup + `initialize` in the constructor.
 - Use context managers (`with Codex() as codex:`) to ensure shutdown.
+- Prefer `thread.run("...")` for the common case. Use `thread.turn(...)` when
+  you need streaming, steering, or interrupt control.
 - For transient overload, use `codex_app_server.retry.retry_on_overload`.