[app-server] feat: v2 Turn APIs (#6216)

Implements:
```
turn/start
turn/interrupt
```

along with their integration tests. These are relatively light wrappers
around the existing core logic, and changes to core logic are minimal.

However, an improvement made for developer ergonomics:
- `turn/start` replaces both `SendUserMessage` (no turn overrides) and
`SendUserTurn` (can override model, approval policy, etc.)

codex-rs/app-server/tests/suite/v2/turn_interrupt.rs

@@ -0,0 +1,128 @@
+#![cfg(unix)]
+
+use anyhow::Result;
+use app_test_support::McpProcess;
+use app_test_support::create_mock_chat_completions_server;
+use app_test_support::create_shell_sse_response;
+use app_test_support::to_response;
+use codex_app_server_protocol::JSONRPCResponse;
+use codex_app_server_protocol::RequestId;
+use codex_app_server_protocol::ThreadStartParams;
+use codex_app_server_protocol::ThreadStartResponse;
+use codex_app_server_protocol::TurnInterruptParams;
+use codex_app_server_protocol::TurnInterruptResponse;
+use codex_app_server_protocol::TurnStartParams;
+use codex_app_server_protocol::TurnStartResponse;
+use codex_app_server_protocol::UserInput as V2UserInput;
+use tempfile::TempDir;
+use tokio::time::timeout;
+
+const DEFAULT_READ_TIMEOUT: std::time::Duration = std::time::Duration::from_secs(10);
+
+#[tokio::test]
+async fn turn_interrupt_aborts_running_turn() -> Result<()> {
+    // Use a portable sleep command to keep the turn running.
+    #[cfg(target_os = "windows")]
+    let shell_command = vec![
+        "powershell".to_string(),
+        "-Command".to_string(),
+        "Start-Sleep -Seconds 10".to_string(),
+    ];
+    #[cfg(not(target_os = "windows"))]
+    let shell_command = vec!["sleep".to_string(), "10".to_string()];
+
+    let tmp = TempDir::new()?;
+    let codex_home = tmp.path().join("codex_home");
+    std::fs::create_dir(&codex_home)?;
+    let working_directory = tmp.path().join("workdir");
+    std::fs::create_dir(&working_directory)?;
+
+    // Mock server: long-running shell command then (after abort) nothing else needed.
+    let server = create_mock_chat_completions_server(vec![create_shell_sse_response(
+        shell_command.clone(),
+        Some(&working_directory),
+        Some(10_000),
+        "call_sleep",
+    )?])
+    .await;
+    create_config_toml(&codex_home, &server.uri())?;
+
+    let mut mcp = McpProcess::new(&codex_home).await?;
+    timeout(DEFAULT_READ_TIMEOUT, mcp.initialize()).await??;
+
+    // Start a v2 thread and capture its id.
+    let thread_req = mcp
+        .send_thread_start_request(ThreadStartParams {
+            model: Some("mock-model".to_string()),
+            ..Default::default()
+        })
+        .await?;
+    let thread_resp: JSONRPCResponse = timeout(
+        DEFAULT_READ_TIMEOUT,
+        mcp.read_stream_until_response_message(RequestId::Integer(thread_req)),
+    )
+    .await??;
+    let ThreadStartResponse { thread } = to_response::<ThreadStartResponse>(thread_resp)?;
+
+    // Start a turn that triggers a long-running command.
+    let turn_req = mcp
+        .send_turn_start_request(TurnStartParams {
+            thread_id: thread.id.clone(),
+            input: vec![V2UserInput::Text {
+                text: "run sleep".to_string(),
+            }],
+            cwd: Some(working_directory.clone()),
+            ..Default::default()
+        })
+        .await?;
+    let turn_resp: JSONRPCResponse = timeout(
+        DEFAULT_READ_TIMEOUT,
+        mcp.read_stream_until_response_message(RequestId::Integer(turn_req)),
+    )
+    .await??;
+    let TurnStartResponse { turn } = to_response::<TurnStartResponse>(turn_resp)?;
+
+    // Give the command a brief moment to start.
+    tokio::time::sleep(std::time::Duration::from_secs(1)).await;
+
+    // Interrupt the in-progress turn by id (v2 API).
+    let interrupt_id = mcp
+        .send_turn_interrupt_request(TurnInterruptParams {
+            thread_id: thread.id,
+            turn_id: turn.id,
+        })
+        .await?;
+    let interrupt_resp: JSONRPCResponse = timeout(
+        DEFAULT_READ_TIMEOUT,
+        mcp.read_stream_until_response_message(RequestId::Integer(interrupt_id)),
+    )
+    .await??;
+    let _resp: TurnInterruptResponse = to_response::<TurnInterruptResponse>(interrupt_resp)?;
+
+    // No fields to assert on; successful deserialization confirms proper response shape.
+    Ok(())
+}
+
+// Helper to create a config.toml pointing at the mock model server.
+fn create_config_toml(codex_home: &std::path::Path, server_uri: &str) -> std::io::Result<()> {
+    let config_toml = codex_home.join("config.toml");
+    std::fs::write(
+        config_toml,
+        format!(
+            r#"
+model = "mock-model"
+approval_policy = "never"
+sandbox_mode = "workspace-write"
+
+model_provider = "mock_provider"
+
+[model_providers.mock_provider]
+name = "Mock provider for test"
+base_url = "{server_uri}/v1"
+wire_api = "chat"
+request_max_retries = 0
+stream_max_retries = 0
+"#
+        ),
+    )
+}