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/core/src/session/session.rs

@@ -364,7 +364,6 @@ impl Session {
         skills_manager: Arc<SkillsManager>,
         plugins_manager: Arc<PluginsManager>,
         mcp_manager: Arc<McpManager>,
-        skills_watcher: Arc<SkillsWatcher>,
         agent_control: AgentControl,
         environment_manager: Arc<EnvironmentManager>,
         analytics_events_client: Option<AnalyticsEventsClient>,
@@ -846,7 +845,6 @@ impl Session {
                 skills_manager,
                 plugins_manager: Arc::clone(&plugins_manager),
                 mcp_manager: Arc::clone(&mcp_manager),
-                skills_watcher,
                 agent_control,
                 network_proxy,
                 network_approval: Arc::clone(&network_approval),
@@ -935,8 +933,6 @@ impl Session {
                 sess.send_event_raw(event).await;
             }
 
-            // Start the watcher after SessionConfigured so it cannot emit earlier events.
-            sess.start_skills_watcher_listener();
             let mut required_mcp_servers: Vec<String> = mcp_servers
                 .iter()
                 .filter(|(_, server)| server.enabled() && server.required())