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/thread_processor.rs

@@ -317,6 +317,7 @@ pub(crate) struct ThreadRequestProcessor {
     pub(super) thread_goal_processor: ThreadGoalRequestProcessor,
     pub(super) state_db: Option<StateDbHandle>,
     pub(super) background_tasks: TaskTracker,
+    pub(super) skills_watcher: Arc<SkillsWatcher>,
 }
 
 impl ThreadRequestProcessor {
@@ -335,6 +336,7 @@ impl ThreadRequestProcessor {
         thread_list_state_permit: Arc<Semaphore>,
         thread_goal_processor: ThreadGoalRequestProcessor,
         state_db: Option<StateDbHandle>,
+        skills_watcher: Arc<SkillsWatcher>,
     ) -> Self {
         Self {
             auth_manager,
@@ -351,6 +353,7 @@ impl ThreadRequestProcessor {
             thread_goal_processor,
             state_db,
             background_tasks: TaskTracker::new(),
+            skills_watcher,
         }
     }
 
@@ -752,6 +755,7 @@ impl ThreadRequestProcessor {
             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),
         }
     }
 
@@ -849,6 +853,7 @@ impl ThreadRequestProcessor {
             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),
         };
         let request_trace = request_context.request_trace();
         let config_manager = self.config_manager.clone();
@@ -1049,7 +1054,6 @@ impl ThreadRequestProcessor {
                 .collect()
         };
         let core_dynamic_tool_count = core_dynamic_tools.len();
-
         let NewThread {
             thread_id,
             thread,