Forward app-server turn clientMetadata to Responses (#16009)

## Summary
App-server v2 already receives turn-scoped `clientMetadata`, but the
Rust app-server was dropping it before the outbound Responses request.
This change keeps the fix lightweight by threading that metadata through
the existing turn-metadata path rather than inventing a new transport.

## What we're trying to do and why
We want turn-scoped metadata from the app-server protocol layer,
especially fields like Hermes/GAAS run IDs, to survive all the way to
the actual Responses API request so it is visible in downstream
websocket request logging and analytics.

The specific bug was:
- app-server protocol uses camelCase `clientMetadata`
- Responses transport already has an existing turn metadata carrier:
`x-codex-turn-metadata`
- websocket transport already rewrites that header into
`request.request_body.client_metadata["x-codex-turn-metadata"]`
- but the Rust app-server never parsed or stored `clientMetadata`, so
nothing from the app-server request was making it into that existing
path

This PR fixes that without adding a new header or a second metadata
channel.

## How we did it
### Protocol surface
- Add optional `clientMetadata` to v2 `TurnStartParams` and
`TurnSteerParams`
- Regenerate the JSON schema / TypeScript fixtures
- Update app-server docs to describe the field and its behavior

### Runtime plumbing
- Add a dedicated core op for app-server user input carrying turn-scoped
metadata: `Op::UserInputWithClientMetadata`
- Wire `turn/start` and `turn/steer` through that op / signature path
instead of dropping the metadata at the message-processor boundary
- Store the metadata in `TurnMetadataState`

### Transport behavior
- Reuse the existing serialized `x-codex-turn-metadata` payload
- Merge the new app-server `clientMetadata` into that JSON additively
- Do **not** replace built-in reserved fields already present in the
turn metadata payload
- Keep websocket behavior unchanged at the outer shape level: it still
sends only `client_metadata["x-codex-turn-metadata"]`, but that JSON
string now contains the merged fields
- Keep HTTP fallback behavior unchanged except that the existing
`x-codex-turn-metadata` header now includes the merged fields too

### Request shape before / after
Before, a websocket `response.create` looked like:
```json
{
  "type": "response.create",
  "client_metadata": {
    "x-codex-turn-metadata": "{\"session_id\":\"...\",\"turn_id\":\"...\"}"
  }
}
```
Even if the app-server caller supplied `clientMetadata`, it was not
represented there.

After, the same request shape is preserved, but the serialized payload
now includes the new turn-scoped fields:
```json
{
  "type": "response.create",
  "client_metadata": {
    "x-codex-turn-metadata": "{\"session_id\":\"...\",\"turn_id\":\"...\",\"fiber_run_id\":\"fiber-start-123\",\"origin\":\"gaas\"}"
  }
}
```

## Validation
### Targeted tests added / updated
- protocol round-trip coverage for `clientMetadata` on `turn/start` and
`turn/steer`
- protocol round-trip coverage for `Op::UserInputWithClientMetadata`
- `TurnMetadataState` merge test proving client metadata is added
without overwriting reserved built-in fields
- websocket request-shape test proving outbound `response.create`
contains merged metadata inside
`client_metadata["x-codex-turn-metadata"]`
- app-server integration tests proving:
- `turn/start` forwards `clientMetadata` into the outbound Responses
request path
  - websocket warmup + real turn request both behave correctly
  - `turn/steer` updates the follow-up request metadata

### Commands run
- `just write-app-server-schema`
- `cargo test -p codex-app-server-protocol`
- `cargo test -p codex-protocol`
- `cargo test -p codex-core
turn_metadata_state_merges_client_metadata_without_replacing_reserved_fields
--lib`
- `cargo test -p codex-core --test all
responses_websocket_preserves_custom_turn_metadata_fields`
- `cargo test -p codex-app-server --test all client_metadata`
- `cargo test -p codex-app-server --test all
turn_start_forwards_client_metadata_to_responses_websocket_request_body_v2
-- --nocapture`
- `just fmt`
- `just fix -p codex-core -p codex-protocol -p codex-app-server-protocol
-p codex-app-server`
- `just fix -p codex-exec -p codex-tui-app-server`
- `just argument-comment-lint`

### Full suite note
`cargo test` in `codex-rs` still fails in:
-
`suite::v2::turn_interrupt::turn_interrupt_resolves_pending_command_approval_request`

I verified that same failure on a clean detached `HEAD` worktree with an
isolated `CARGO_TARGET_DIR`, so it is not caused by this patch.

codex-rs/core/tests/suite/otel.rs

@@ -107,6 +107,7 @@ async fn responses_api_emits_api_request_event() {
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -150,6 +151,7 @@ async fn process_sse_emits_tracing_for_output_item() {
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -193,6 +195,7 @@ async fn process_sse_emits_failed_event_on_parse_error() {
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -237,6 +240,7 @@ async fn process_sse_records_failed_event_when_stream_closes_without_completed()
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -301,6 +305,7 @@ async fn process_sse_failed_event_records_response_error_message() {
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -363,6 +368,7 @@ async fn process_sse_failed_event_logs_parse_error() {
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -412,6 +418,7 @@ async fn process_sse_failed_event_logs_missing_error() {
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -470,6 +477,7 @@ async fn process_sse_failed_event_logs_response_completed_parse_error() {
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -522,6 +530,7 @@ async fn process_sse_emits_completed_telemetry() {
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -594,6 +603,7 @@ async fn handle_responses_span_records_response_kind_and_tool_name() {
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -678,6 +688,7 @@ async fn record_responses_sets_span_fields_for_response_events() {
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -762,6 +773,7 @@ async fn handle_response_item_records_tool_result_for_custom_tool_call() {
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -835,6 +847,7 @@ async fn handle_response_item_records_tool_result_for_function_call() {
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -918,6 +931,7 @@ async fn handle_response_item_records_tool_result_for_local_shell_missing_ids()
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -986,6 +1000,7 @@ async fn handle_response_item_records_tool_result_for_local_shell_call() {
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -1094,6 +1109,7 @@ async fn handle_container_exec_autoapprove_from_config_records_tool_decision() {
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -1145,6 +1161,7 @@ async fn handle_container_exec_user_approved_records_tool_decision() {
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -1211,6 +1228,7 @@ async fn handle_container_exec_user_approved_for_session_records_tool_decision()
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -1277,6 +1295,7 @@ async fn handle_sandbox_error_user_approves_retry_records_tool_decision() {
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -1343,6 +1362,7 @@ async fn handle_container_exec_user_denies_records_tool_decision() {
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -1409,6 +1429,7 @@ async fn handle_sandbox_error_user_approves_for_session_records_tool_decision()
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();
@@ -1476,6 +1497,7 @@ async fn handle_sandbox_error_user_denies_records_tool_decision() {
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await
         .unwrap();