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/src/codex_tests.rs

@@ -1331,6 +1331,7 @@ async fn fork_startup_context_then_first_turn_diff_snapshot() -> anyhow::Result<
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await?;
     wait_for_event(&initial.codex, |ev| matches!(ev, EventMsg::TurnComplete(_))).await;
@@ -1386,6 +1387,7 @@ async fn fork_startup_context_then_first_turn_diff_snapshot() -> anyhow::Result<
                 text_elements: Vec::new(),
             }],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         })
         .await?;
     wait_for_event(&forked.thread, |ev| matches!(ev, EventMsg::TurnComplete(_))).await;
@@ -3279,6 +3281,7 @@ fn op_kind_distinguishes_turn_ops() {
         Op::UserInput {
             items: vec![],
             final_output_json_schema: None,
+            responsesapi_client_metadata: None,
         }
         .kind(),
         "user_input"
@@ -4857,7 +4860,9 @@ async fn steer_input_requires_active_turn() {
     }];
 
     let err = sess
-        .steer_input(input, /*expected_turn_id*/ None)
+        .steer_input(
+            input, /*expected_turn_id*/ None, /*responsesapi_client_metadata*/ None,
+        )
         .await
         .expect_err("steering without active turn should fail");
 
@@ -4886,7 +4891,11 @@ async fn steer_input_enforces_expected_turn_id() {
         text_elements: Vec::new(),
     }];
     let err = sess
-        .steer_input(steer_input, Some("different-turn-id"))
+        .steer_input(
+            steer_input,
+            Some("different-turn-id"),
+            /*responsesapi_client_metadata*/ None,
+        )
         .await
         .expect_err("mismatched expected turn id should fail");
 
@@ -4928,7 +4937,11 @@ async fn steer_input_rejects_non_regular_turns() {
             text_elements: Vec::new(),
         }];
         let err = sess
-            .steer_input(steer_input, /*expected_turn_id*/ None)
+            .steer_input(
+                steer_input,
+                /*expected_turn_id*/ None,
+                /*responsesapi_client_metadata*/ None,
+            )
             .await
             .expect_err("steering a non-regular turn should fail");
 
@@ -4960,7 +4973,11 @@ async fn steer_input_returns_active_turn_id() {
         text_elements: Vec::new(),
     }];
     let turn_id = sess
-        .steer_input(steer_input, Some(&tc.sub_id))
+        .steer_input(
+            steer_input,
+            Some(&tc.sub_id),
+            /*responsesapi_client_metadata*/ None,
+        )
         .await
         .expect("steering with matching expected turn id should succeed");
 
@@ -5147,6 +5164,7 @@ async fn steered_input_reopens_mailbox_delivery_for_current_turn() {
             text_elements: Vec::new(),
         }],
         Some(&tc.sub_id),
+        /*responsesapi_client_metadata*/ None,
     )
     .await
     .expect("steered input should be accepted");
@@ -5191,6 +5209,7 @@ async fn stale_defer_mailbox_delivery_does_not_override_steered_input() {
             text_elements: Vec::new(),
         }],
         Some(&tc.sub_id),
+        /*responsesapi_client_metadata*/ None,
     )
     .await
     .expect("steered input should be accepted");