Make the agents overview an interactive task dashboard (#39112)

## What changed

- Let users start tasks, open root sessions, rename tasks, and stop active work directly from the agents overview.
- Show details for the selected task on wide terminals and limit the overview to root sessions while still reflecting background activity.
- Preserve draft input and pending server requests when switching sessions so running roots and their subagents can continue in the background.
- Apply the selected project's working directory when dispatching from project grouping, including remote workspaces.

## Testing

- Expand overview rendering and interaction coverage for root filtering, dispatch, search, selection, renaming, and responsive input.
- Cover switching away from roots with running subagents and retaining background server requests.

GitOrigin-RevId: b7b0d33b7ecc077498efb756a0ad2fd425158b17

codex-rs/tui/src/app_server_session.rs

@@ -602,21 +602,24 @@ impl AppServerSession {
 
     #[cfg(test)]
     pub(crate) async fn start_thread(&mut self, config: &Config) -> Result<AppServerStartedThread> {
-        self.start_thread_with_session_start_source(config, /*session_start_source*/ None)
-            .await
+        self.start_thread_with_session_start_source(
+            config, /*session_start_source*/ None, /*remote_cwd_override*/ None,
+        )
+        .await
     }
 
     pub(crate) async fn start_thread_with_session_start_source(
         &mut self,
         config: &Config,
         session_start_source: Option<ThreadStartSource>,
+        remote_cwd_override: Option<&std::path::Path>,
     ) -> Result<AppServerStartedThread> {
         let request_id = self.next_request_id();
         let session_config = self.session_config_with_effective_service_tier(config);
         let mut params = thread_start_params_from_config(
             &session_config,
             self.thread_params_mode(),
-            self.remote_cwd_override.as_deref(),
+            remote_cwd_override.or(self.remote_cwd_override.as_deref()),
             session_start_source,
         );
         if self.history_support == ThreadHistorySupport::LegacyOnly {