Reapply "Move skills watcher to app-server" (#21652)

## Why

PR #21460 reverted the earlier move of skills change watching from
`codex-core` into app-server. This reapplies that boundary change so
app-server owns client-facing `skills/changed` notifications and core no
longer carries the watcher.

## What

- Restore the app-server `SkillsWatcher` and register it from thread
listener setup.
- Remove the core-owned skills watcher and its core live-reload
integration surface.
- Restore app-server coverage for `skills/changed` notifications after a
watched skill file changes.

## Validation

- `cargo test -p codex-app-server --test all
suite::v2::skills_list::skills_changed_notification_is_emitted_after_skill_change
-- --exact --nocapture`
- `cargo test -p codex-core --lib --no-run`

codex-rs/app-server/src/message_processor.rs

@@ -36,6 +36,7 @@ use crate::request_processors::WindowsSandboxRequestProcessor;
 use crate::request_serialization::QueuedInitializedRequest;
 use crate::request_serialization::RequestSerializationQueueKey;
 use crate::request_serialization::RequestSerializationQueues;
+use crate::skills_watcher::SkillsWatcher;
 use crate::thread_state::ConnectionCapabilities;
 use crate::thread_state::ThreadStateManager;
 use crate::transport::AppServerTransport;
@@ -314,6 +315,7 @@ impl MessageProcessor {
         thread_manager
             .plugins_manager()
             .set_analytics_events_client(analytics_events_client.clone());
+        let skills_watcher = SkillsWatcher::new(thread_manager.skills_manager(), outgoing.clone());
 
         let pending_thread_unloads = Arc::new(Mutex::new(HashSet::new()));
         let thread_watch_manager =
@@ -405,6 +407,7 @@ impl MessageProcessor {
             Arc::clone(&thread_list_state_permit),
             thread_goal_processor.clone(),
             state_db,
+            Arc::clone(&skills_watcher),
         );
         let turn_processor = TurnRequestProcessor::new(
             auth_manager.clone(),
@@ -418,6 +421,7 @@ impl MessageProcessor {
             thread_state_manager,
             thread_watch_manager,
             thread_list_state_permit,
+            Arc::clone(&skills_watcher),
         );
         if matches!(plugin_startup_tasks, crate::PluginStartupTasks::Start) {
             // Keep plugin startup warmups aligned at app-server startup.