[codex] Split Python SDK helper logic (#22939)

## Summary
- Move approval-mode mapping into
`sdk/python/src/openai_codex/_approval_mode.py`.
- Move initialize metadata parsing and normalization into
`sdk/python/src/openai_codex/_initialize_metadata.py`.
- Keep the public `ApprovalMode` export stable and retarget direct
metadata helper coverage.

## Integration coverage
- Add an app-server harness smoke that exercises sync and async SDK
initialization plus thread creation.

## Validation
- Local tests were not run per repo guidance. CI should validate this
branch once the PR is online.

sdk/python/src/openai_codex/_approval_mode.py

@@ -0,0 +1,51 @@
+from __future__ import annotations
+
+from enum import Enum
+from typing import NoReturn
+
+from .generated.v2_all import (
+    ApprovalsReviewer,
+    AskForApproval,
+    AskForApprovalValue,
+)
+
+
+class ApprovalMode(str, Enum):
+    """High-level approval behavior for escalated permission requests."""
+
+    deny_all = "deny_all"
+    auto_review = "auto_review"
+
+
+def _approval_mode_settings(
+    approval_mode: ApprovalMode,
+) -> tuple[AskForApproval, ApprovalsReviewer | None]:
+    """Map the public approval mode to generated app-server start params."""
+    if not isinstance(approval_mode, ApprovalMode):
+        supported = ", ".join(mode.value for mode in ApprovalMode)
+        raise ValueError(f"approval_mode must be one of: {supported}")
+
+    match approval_mode:
+        case ApprovalMode.auto_review:
+            return (
+                AskForApproval(root=AskForApprovalValue.on_request),
+                ApprovalsReviewer.auto_review,
+            )
+        case ApprovalMode.deny_all:
+            return AskForApproval(root=AskForApprovalValue.never), None
+        case _:
+            return _assert_never_approval_mode(approval_mode)
+
+
+def _assert_never_approval_mode(approval_mode: NoReturn) -> NoReturn:
+    """Make approval mode mapping exhaustive for static type checkers."""
+    raise AssertionError(f"Unhandled approval mode: {approval_mode!r}")
+
+
+def _approval_mode_override_settings(
+    approval_mode: ApprovalMode | None,
+) -> tuple[AskForApproval | None, ApprovalsReviewer | None]:
+    """Map an optional public approval mode to app-server override params."""
+    if approval_mode is None:
+        return None, None
+    return _approval_mode_settings(approval_mode)