[2/8] Support piped stdin in exec process API (#18086)

## Summary
- Add an explicit stdin mode to process/start.
- Keep normal non-interactive exec stdin closed while allowing
pipe-backed processes.

## Stack
```text
o  #18027 [8/8] Fail exec client operations after disconnect
│
o  #18025 [7/8] Cover MCP stdio tests with executor placement
│
o  #18089 [6/8] Wire remote MCP stdio through executor
│
o  #18088 [5/8] Add executor process transport for MCP stdio
│
o  #18087 [4/8] Abstract MCP stdio server launching
│
o  #18020 [3/8] Add pushed exec process events
│
@  #18086 [2/8] Support piped stdin in exec process API
│
o  #18085 [1/8] Add MCP server environment config
│
o  main
```

Co-authored-by: Codex <noreply@openai.com>

codex-rs/exec-server/tests/process.rs

@@ -10,6 +10,8 @@ use codex_exec_server::InitializeResponse;
 use codex_exec_server::ProcessId;
 use codex_exec_server::ReadResponse;
 use codex_exec_server::TerminateResponse;
+use codex_exec_server::WriteResponse;
+use codex_exec_server::WriteStatus;
 use common::exec_server::exec_server;
 use pretty_assertions::assert_eq;
 
@@ -47,6 +49,7 @@ async fn exec_server_starts_process_over_websocket() -> anyhow::Result<()> {
                 "cwd": std::env::current_dir()?,
                 "env": {},
                 "tty": false,
+                "pipeStdin": false,
                 "arg0": null
             }),
         )
@@ -75,6 +78,99 @@ async fn exec_server_starts_process_over_websocket() -> anyhow::Result<()> {
     Ok(())
 }
 
+#[tokio::test(flavor = "multi_thread", worker_threads = 2)]
+async fn exec_server_defaults_omitted_pipe_stdin_to_closed_stdin() -> anyhow::Result<()> {
+    let mut server = exec_server().await?;
+    let initialize_id = server
+        .send_request(
+            "initialize",
+            serde_json::to_value(InitializeParams {
+                client_name: "exec-server-test".to_string(),
+                resume_session_id: None,
+            })?,
+        )
+        .await?;
+    let _ = server
+        .wait_for_event(|event| {
+            matches!(
+                event,
+                JSONRPCMessage::Response(JSONRPCResponse { id, .. }) if id == &initialize_id
+            )
+        })
+        .await?;
+
+    server
+        .send_notification("initialized", serde_json::json!({}))
+        .await?;
+
+    let process_start_id = server
+        .send_request(
+            "process/start",
+            serde_json::json!({
+                "processId": "proc-default-stdin",
+                "argv": [
+                    "/bin/sh",
+                    "-c",
+                    "sleep 0.3; if IFS= read -r line; then printf 'read:%s\\n' \"$line\"; else printf 'eof\\n'; fi"
+                ],
+                "cwd": std::env::current_dir()?,
+                "env": {},
+                "tty": false,
+                "arg0": null
+            }),
+        )
+        .await?;
+    let response = server
+        .wait_for_event(|event| {
+            matches!(
+                event,
+                JSONRPCMessage::Response(JSONRPCResponse { id, .. }) if id == &process_start_id
+            )
+        })
+        .await?;
+    let JSONRPCMessage::Response(JSONRPCResponse { result, .. }) = response else {
+        panic!("expected process/start response");
+    };
+    let process_start_response: ExecResponse = serde_json::from_value(result)?;
+    assert_eq!(
+        process_start_response,
+        ExecResponse {
+            process_id: ProcessId::from("proc-default-stdin")
+        }
+    );
+
+    let write_id = server
+        .send_request(
+            "process/write",
+            serde_json::json!({
+                "processId": "proc-default-stdin",
+                "chunk": "aWdub3JlZAo="
+            }),
+        )
+        .await?;
+    let response = server
+        .wait_for_event(|event| {
+            matches!(
+                event,
+                JSONRPCMessage::Response(JSONRPCResponse { id, .. }) if id == &write_id
+            )
+        })
+        .await?;
+    let JSONRPCMessage::Response(JSONRPCResponse { result, .. }) = response else {
+        panic!("expected process/write response");
+    };
+    let write_response: WriteResponse = serde_json::from_value(result)?;
+    assert_eq!(
+        write_response,
+        WriteResponse {
+            status: WriteStatus::StdinClosed
+        }
+    );
+
+    server.shutdown().await?;
+    Ok(())
+}
+
 #[tokio::test(flavor = "multi_thread", worker_threads = 2)]
 async fn exec_server_resumes_detached_session_without_killing_processes() -> anyhow::Result<()> {
     let mut server = exec_server().await?;
@@ -113,6 +209,7 @@ async fn exec_server_resumes_detached_session_without_killing_processes() -> any
                 "cwd": std::env::current_dir()?,
                 "env": {},
                 "tty": false,
+                "pipeStdin": false,
                 "arg0": null
             }),
         )