Add Python SDK public API and examples (#14446)

## TL;DR
WIP esp the examples

Thin the Python SDK public surface so the wrapper layer returns
canonical app-server generated models directly.

- keeps `Codex` / `AsyncCodex` / `Thread` / `Turn` and input helpers,
but removes alias-only type layers and custom result models
- `metadata` now returns `InitializeResponse` and `run()` returns the
generated app-server `Turn`
- updates docs, examples, notebook, and tests to use canonical generated
types and regenerates `v2_all.py` against current schema
- keeps the pinned runtime-package integration flow and real integration
coverage

  ## Validation
  - `PYTHONPATH=sdk/python/src python3 -m pytest sdk/python/tests`
- `GH_TOKEN="$(gh auth token)" RUN_REAL_CODEX_TESTS=1
PYTHONPATH=sdk/python/src python3 -m pytest sdk/python/tests -rs`

---------

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

sdk/python/examples/12_turn_params_kitchen_sink/sync.py

@@ -0,0 +1,78 @@
+import json
+import sys
+from pathlib import Path
+
+_EXAMPLES_ROOT = Path(__file__).resolve().parents[1]
+if str(_EXAMPLES_ROOT) not in sys.path:
+    sys.path.insert(0, str(_EXAMPLES_ROOT))
+
+from _bootstrap import (
+    assistant_text_from_turn,
+    ensure_local_sdk_src,
+    find_turn_by_id,
+    runtime_config,
+)
+
+ensure_local_sdk_src()
+
+from codex_app_server import (
+    AskForApproval,
+    Codex,
+    Personality,
+    ReasoningSummary,
+    TextInput,
+)
+
+OUTPUT_SCHEMA = {
+    "type": "object",
+    "properties": {
+        "summary": {"type": "string"},
+        "actions": {
+            "type": "array",
+            "items": {"type": "string"},
+        },
+    },
+    "required": ["summary", "actions"],
+    "additionalProperties": False,
+}
+
+SUMMARY = ReasoningSummary.model_validate("concise")
+
+PROMPT = (
+    "Analyze a safe rollout plan for enabling a feature flag in production. "
+    "Return JSON matching the requested schema."
+)
+APPROVAL_POLICY = AskForApproval.model_validate("never")
+
+with Codex(config=runtime_config()) as codex:
+    thread = codex.thread_start(model="gpt-5.4", config={"model_reasoning_effort": "high"})
+
+    turn = thread.turn(
+        TextInput(PROMPT),
+        approval_policy=APPROVAL_POLICY,
+        output_schema=OUTPUT_SCHEMA,
+        personality=Personality.pragmatic,
+        summary=SUMMARY,
+    )
+    result = turn.run()
+    persisted = thread.read(include_turns=True)
+    persisted_turn = find_turn_by_id(persisted.thread.turns, result.id)
+    structured_text = assistant_text_from_turn(persisted_turn).strip()
+    try:
+        structured = json.loads(structured_text)
+    except json.JSONDecodeError as exc:
+        raise RuntimeError(f"Expected JSON matching OUTPUT_SCHEMA, got: {structured_text!r}") from exc
+
+    summary = structured.get("summary")
+    actions = structured.get("actions")
+    if not isinstance(summary, str) or not isinstance(actions, list) or not all(
+        isinstance(action, str) for action in actions
+    ):
+        raise RuntimeError(f"Expected structured output with string summary/actions, got: {structured!r}")
+
+    print("Status:", result.status)
+    print("summary:", summary)
+    print("actions:")
+    for action in actions:
+        print("-", action)
+    print("Items:", 0 if persisted_turn is None else len(persisted_turn.items or []))