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/request_processors/turn_processor.rs

@@ -13,6 +13,7 @@ pub(crate) struct TurnRequestProcessor {
     thread_state_manager: ThreadStateManager,
     thread_watch_manager: ThreadWatchManager,
     thread_list_state_permit: Arc<Semaphore>,
+    skills_watcher: Arc<SkillsWatcher>,
 }
 
 impl TurnRequestProcessor {
@@ -29,6 +30,7 @@ impl TurnRequestProcessor {
         thread_state_manager: ThreadStateManager,
         thread_watch_manager: ThreadWatchManager,
         thread_list_state_permit: Arc<Semaphore>,
+        skills_watcher: Arc<SkillsWatcher>,
     ) -> Self {
         Self {
             auth_manager,
@@ -42,6 +44,7 @@ impl TurnRequestProcessor {
             thread_state_manager,
             thread_watch_manager,
             thread_list_state_permit,
+            skills_watcher,
         }
     }
 
@@ -1087,6 +1090,7 @@ impl TurnRequestProcessor {
             thread_list_state_permit: self.thread_list_state_permit.clone(),
             fallback_model_provider: self.config.model_provider_id.clone(),
             codex_home: self.config.codex_home.to_path_buf(),
+            skills_watcher: Arc::clone(&self.skills_watcher),
         }
     }