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/app-server/src/transport/remote_control/tests.rs

@@ -106,13 +106,10 @@ async fn remote_control_state_runtime(codex_home: &TempDir) -> Arc<StateRuntime>
 }
 
 fn remote_control_url_for_listener(listener: &TcpListener) -> String {
-    format!(
-        "http://localhost:{}/backend-api/",
-        listener
-            .local_addr()
-            .expect("listener should have a local addr")
-            .port()
-    )
+    let addr = listener
+        .local_addr()
+        .expect("listener should have a local addr");
+    format!("http://{addr}/backend-api/")
 }
 
 #[tokio::test]

codex-rs/app-server/src/transport/remote_control/websocket.rs

@@ -931,13 +931,10 @@ mod tests {
     }
 
     fn remote_control_url_for_listener(listener: &TcpListener) -> String {
-        format!(
-            "http://localhost:{}/backend-api/",
-            listener
-                .local_addr()
-                .expect("listener should have a local addr")
-                .port()
-        )
+        let addr = listener
+            .local_addr()
+            .expect("listener should have a local addr");
+        format!("http://{addr}/backend-api/")
     }
 
     fn remote_control_auth_dot_json(access_token: &str) -> AuthDotJson {
@@ -1041,14 +1038,6 @@ mod tests {
         let remote_control_url = remote_control_url_for_listener(&listener);
         let remote_control_target =
             normalize_remote_control_url(&remote_control_url).expect("target should parse");
-        let server_task = tokio::spawn(async move {
-            let (stream, request_line) = accept_http_request(&listener).await;
-            assert_eq!(
-                request_line,
-                "GET /backend-api/wham/remote/control/server HTTP/1.1"
-            );
-            respond_with_status_and_headers(stream, "401 Unauthorized", &[], "unauthorized").await;
-        });
         let codex_home = TempDir::new().expect("temp dir should create");
         save_auth(
             codex_home.path(),
@@ -1076,6 +1065,15 @@ mod tests {
         )
         .expect("fresh auth should save");
 
+        let server_task = tokio::spawn(async move {
+            let (stream, request_line) = accept_http_request(&listener).await;
+            assert_eq!(
+                request_line,
+                "GET /backend-api/wham/remote/control/server HTTP/1.1"
+            );
+            respond_with_status_and_headers(stream, "401 Unauthorized", &[], "unauthorized").await;
+        });
+
         let err = connect_remote_control_websocket(
             &remote_control_target,
             Some(state_db.as_ref()),