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/client.rs

@@ -290,6 +290,7 @@ async fn resume_includes_initial_messages_and_sends_prior_items() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -365,6 +366,7 @@ async fn includes_conversation_id_and_model_headers_in_request() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -424,6 +426,7 @@ async fn includes_base_instructions_override_in_request() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -488,6 +491,7 @@ async fn chatgpt_auth_sends_correct_request() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -582,6 +586,7 @@ async fn prefers_apikey_when_config_prefers_apikey_even_with_chatgpt_tokens() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -622,6 +627,7 @@ async fn includes_user_instructions_message_in_request() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -692,6 +698,7 @@ async fn skills_append_to_instructions() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -741,6 +748,7 @@ async fn includes_configured_effort_in_request() -> anyhow::Result<()> {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -777,6 +785,7 @@ async fn includes_no_effort_in_request() -> anyhow::Result<()> {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -811,6 +820,7 @@ async fn includes_default_reasoning_effort_in_request_when_defined_by_model_fami
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -849,6 +859,7 @@ async fn configured_reasoning_summary_is_sent() -> anyhow::Result<()> {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -887,6 +898,7 @@ async fn reasoning_summary_is_omitted_when_disabled() -> anyhow::Result<()> {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -919,6 +931,7 @@ async fn includes_default_verbosity_in_request() -> anyhow::Result<()> {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -958,6 +971,7 @@ async fn configured_verbosity_not_sent_for_models_without_support() -> anyhow::R
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -996,6 +1010,7 @@ async fn configured_verbosity_is_sent() -> anyhow::Result<()> {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -1050,6 +1065,7 @@ async fn includes_developer_instructions_message_in_request() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -1280,6 +1296,7 @@ async fn token_count_includes_rate_limits_snapshot() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -1437,6 +1454,7 @@ async fn usage_limit_error_emits_rate_limit_event() -> anyhow::Result<()> {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .expect("submission should succeed while emitting usage limit error events");
@@ -1506,6 +1524,7 @@ async fn context_window_error_sets_total_tokens_to_model_window() -> anyhow::Res
             items: vec![UserInput::Text {
                 text: "seed turn".into(),
             }],
+            final_output_json_schema: None,
         })
         .await?;
 
@@ -1516,6 +1535,7 @@ async fn context_window_error_sets_total_tokens_to_model_window() -> anyhow::Res
             items: vec![UserInput::Text {
                 text: "trigger context window".into(),
             }],
+            final_output_json_schema: None,
         })
         .await?;
 
@@ -1635,6 +1655,7 @@ async fn azure_overrides_assign_properties_used_for_responses_url() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -1717,6 +1738,7 @@ async fn env_var_overrides_loaded_auth() {
             items: vec![UserInput::Text {
                 text: "hello".into(),
             }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -1800,6 +1822,7 @@ async fn history_dedupes_streamed_and_final_messages_across_turns() {
     codex
         .submit(Op::UserInput {
             items: vec![UserInput::Text { text: "U1".into() }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -1809,6 +1832,7 @@ async fn history_dedupes_streamed_and_final_messages_across_turns() {
     codex
         .submit(Op::UserInput {
             items: vec![UserInput::Text { text: "U2".into() }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();
@@ -1818,6 +1842,7 @@ async fn history_dedupes_streamed_and_final_messages_across_turns() {
     codex
         .submit(Op::UserInput {
             items: vec![UserInput::Text { text: "U3".into() }],
+            final_output_json_schema: None,
         })
         .await
         .unwrap();