feat: expose outputSchema to user_turn/turn_start app_server API

[apanasenko-oai]

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

[pakrym-oai]

we have this value on the UserTurn, should we use that instead? I'd like to remove UserInput all together. They call the same codepath eventually anyway.

[pakrym-oai]

Adding final_output_json_schema to UserInput isn't great but we should've unified it with UserTurn a long time ago.