feat: expose outputSchema to user_turn/turn_start app_server API (#8377)

What changed
- Added `outputSchema` support to the app-server APIs, mirroring `codex
exec --output-schema` behavior.
- V1 `sendUserTurn` now accepts `outputSchema` and constrains the final
assistant message for that turn.
- V2 `turn/start` now accepts `outputSchema` and constrains the final
assistant message for that turn (explicitly per-turn only).

Core behavior
- `Op::UserTurn` already supported `final_output_json_schema`; now V1
`sendUserTurn` forwards `outputSchema` into that field.
- `Op::UserInput` now carries `final_output_json_schema` for per-turn
settings updates; core maps it into
`SessionSettingsUpdate.final_output_json_schema` so it applies to the
created turn context.
- V2 `turn/start` does NOT persist the schema via `OverrideTurnContext`
(it’s applied only for the current turn). Other overrides
(cwd/model/etc) keep their existing persistent behavior.

API / docs
- `codex-rs/app-server-protocol/src/protocol/v1.rs`: add `output_schema:
Option<serde_json::Value>` to `SendUserTurnParams` (serialized as
`outputSchema`).
- `codex-rs/app-server-protocol/src/protocol/v2.rs`: add `output_schema:
Option<JsonValue>` to `TurnStartParams` (serialized as `outputSchema`).
- `codex-rs/app-server/README.md`: document `outputSchema` for
`turn/start` and clarify it applies only to the current turn.
- `codex-rs/docs/codex_mcp_interface.md`: document `outputSchema` for v1
`sendUserTurn` and v2 `turn/start`.

Tests added/updated
- New app-server integration tests asserting `outputSchema` is forwarded
into outbound `/responses` requests as `text.format`:
  - `codex-rs/app-server/tests/suite/output_schema.rs`
  - `codex-rs/app-server/tests/suite/v2/output_schema.rs`
- Added per-turn semantics tests (schema does not leak to the next
turn):
  - `send_user_turn_output_schema_is_per_turn_v1`
  - `turn_start_output_schema_is_per_turn_v2`
- Added protocol wire-compat tests for the merged op:
  - serialize omits `final_output_json_schema` when `None`
  - deserialize works when field is missing
  - serialize includes `final_output_json_schema` when `Some(schema)`

Call site updates (high level)
- Updated all `Op::UserInput { .. }` constructions to include
`final_output_json_schema`:
  - `codex-rs/app-server/src/codex_message_processor.rs`
  - `codex-rs/core/src/codex_delegate.rs`
  - `codex-rs/mcp-server/src/codex_tool_runner.rs`
  - `codex-rs/tui/src/chatwidget.rs`
  - `codex-rs/tui2/src/chatwidget.rs`
  - plus impacted core tests.

Validation
- `just fmt`
- `cargo test -p codex-core`
- `cargo test -p codex-app-server`
- `cargo test -p codex-mcp-server`
- `cargo test -p codex-tui`
- `cargo test -p codex-tui2`
- `cargo test -p codex-protocol`
- `cargo clippy --all-features --tests --profile dev --fix -- -D
warnings`

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

@@ -46,6 +46,7 @@ async fn responses_api_emits_api_request_event() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -87,6 +88,7 @@ async fn process_sse_emits_tracing_for_output_item() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -125,6 +127,7 @@ async fn process_sse_emits_failed_event_on_parse_error() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -164,6 +167,7 @@ async fn process_sse_records_failed_event_when_stream_closes_without_completed()
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -223,6 +227,7 @@ async fn process_sse_failed_event_records_response_error_message() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -280,6 +285,7 @@ async fn process_sse_failed_event_logs_parse_error() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -324,6 +330,7 @@ async fn process_sse_failed_event_logs_missing_error() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -377,6 +384,7 @@ async fn process_sse_failed_event_logs_response_completed_parse_error() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -427,6 +435,7 @@ async fn process_sse_emits_completed_telemetry() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -494,6 +503,7 @@ async fn handle_responses_span_records_response_kind_and_tool_name() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -558,6 +568,7 @@ async fn record_responses_sets_span_fields_for_response_events() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -637,6 +648,7 @@ async fn handle_response_item_records_tool_result_for_custom_tool_call() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -704,6 +716,7 @@ async fn handle_response_item_records_tool_result_for_function_call() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -781,6 +794,7 @@ async fn handle_response_item_records_tool_result_for_local_shell_missing_ids()
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -842,6 +856,7 @@ async fn handle_response_item_records_tool_result_for_local_shell_call() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -946,6 +961,7 @@ async fn handle_container_exec_autoapprove_from_config_records_tool_decision() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -994,6 +1010,7 @@ async fn handle_container_exec_user_approved_records_tool_decision() {
             items: vec![UserInput::Text {
                 text: "approved".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -1052,6 +1069,7 @@ async fn handle_container_exec_user_approved_for_session_records_tool_decision()
             items: vec![UserInput::Text {
                 text: "persist".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -1110,6 +1128,7 @@ async fn handle_sandbox_error_user_approves_retry_records_tool_decision() {
             items: vec![UserInput::Text {
                 text: "retry".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -1168,6 +1187,7 @@ async fn handle_container_exec_user_denies_records_tool_decision() {
             items: vec![UserInput::Text {
                 text: "deny".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -1226,6 +1246,7 @@ async fn handle_sandbox_error_user_approves_for_session_records_tool_decision()
             items: vec![UserInput::Text {
                 text: "persist".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -1285,6 +1306,7 @@ async fn handle_sandbox_error_user_denies_records_tool_decision() {
             items: vec![UserInput::Text {
                 text: "deny".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();