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/codex_delegate.rs

@@ -83,7 +83,6 @@ pub(crate) async fn run_codex_thread_interactive(
         skills_manager: Arc::clone(&parent_session.services.skills_manager),
         plugins_manager: Arc::clone(&parent_session.services.plugins_manager),
         mcp_manager: Arc::clone(&parent_session.services.mcp_manager),
-        skills_watcher: Arc::clone(&parent_session.services.skills_watcher),
         conversation_history: initial_history.unwrap_or(InitialHistory::New),
         session_source: SessionSource::SubAgent(subagent_source.clone()),
         thread_source: Some(ThreadSource::Subagent),