refactor(host): move chat_spawn to op-web-daemon (Phase 2 leaf)

Process-spawn helpers (find_binary / build_command / exit_status_label) for the
CLI chat bridges. Promoted to pub; consumers chat_http_server + chat_subprocess
repointed to op_web_daemon::chat_spawn. No new deps (no Cargo.lock change).

crates/op-host-desktop/src/chat_http_server.rs

@@ -41,7 +41,7 @@ use tokio::io::{AsyncBufReadExt, BufReader};
 use tokio::sync::mpsc;
 
 use crate::chat_runtime::{shared_runtime, BlockingRecvIter};
-use crate::chat_spawn::{build_command, find_binary};
+use op_web_daemon::chat_spawn::{build_command, find_binary};
 
 /// TS `opencode-client.ts` reuses an existing server on the default
 /// port before spawning its own.

crates/op-host-desktop/src/chat_subprocess.rs

@@ -63,7 +63,7 @@ use tokio::io::{AsyncBufReadExt, BufReader};
 use tokio::sync::mpsc;
 
 use crate::chat_runtime::{prompt_with_system_prompt, shared_runtime, BlockingRecvIter};
-use crate::chat_spawn::{build_command, exit_status_label, find_binary};
+use op_web_daemon::chat_spawn::{build_command, exit_status_label, find_binary};
 use crate::chat_subprocess_quirks as quirks;
 
 /// How the user's prompt reaches the CLI. Claude Code's `--print`

crates/op-host-desktop/src/main.rs

@@ -19,7 +19,6 @@ mod chat_intent;
 mod chat_provider_llm;
 mod chat_runtime;
 mod chat_session;
-mod chat_spawn;
 mod chat_subprocess;
 mod chat_subprocess_quirks;
 mod chat_system_prompt;

crates/op-web-daemon/src/chat_spawn.rs

@@ -18,7 +18,7 @@ use tokio::process::Command;
 ///
 /// Cross-platform: each branch only probes paths that exist on that
 /// OS so we don't pay for filesystem-stat misses on the wrong OS.
-pub(crate) fn find_binary(name: &str) -> String {
+pub fn find_binary(name: &str) -> String {
     // PATH-relative entries first (cross-platform).
     if let Ok(path_env) = std::env::var("PATH") {
         let sep = if cfg!(windows) { ';' } else { ':' };
@@ -122,7 +122,7 @@ fn well_known_install_paths(name: &str) -> Vec<PathBuf> {
 /// Unix so Ctrl-C in the OP terminal doesn't kill the CLI; on Windows
 /// `creation_flags(CREATE_NO_WINDOW)` so spawning the CLI doesn't
 /// pop a console window for users running the GUI build).
-pub(crate) fn build_command(binary: &str, args: &[String]) -> Command {
+pub fn build_command(binary: &str, args: &[String]) -> Command {
     #[cfg(windows)]
     {
         // CREATE_NO_WINDOW from winbase.h — keeps the console hidden
@@ -173,7 +173,7 @@ pub(crate) fn build_command(binary: &str, args: &[String]) -> Command {
 /// Stringify an `ExitStatus` for chat error reporting. Cross-platform:
 /// on Unix `.code()` is `None` when killed by signal — show the signal
 /// number instead; on Windows `.code()` is always populated.
-pub(crate) fn exit_status_label(status: &std::process::ExitStatus) -> String {
+pub fn exit_status_label(status: &std::process::ExitStatus) -> String {
     if let Some(code) = status.code() {
         return code.to_string();
     }

crates/op-web-daemon/src/lib.rs

@@ -14,4 +14,5 @@
 //! `op-host-web-server` binary depend on this crate.
 
 // Phase 2 — host-free leaf modules.
+pub mod chat_spawn;
 pub mod web_static;