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/turn.rs

@@ -1505,7 +1505,6 @@ pub(super) fn realtime_text_for_event(msg: &EventMsg) -> Option<String> {
         | EventMsg::StreamError(_)
         | EventMsg::TurnDiff(_)
         | EventMsg::RealtimeConversationListVoicesResponse(_)
-        | EventMsg::SkillsUpdateAvailable
         | EventMsg::PlanUpdate(_)
         | EventMsg::TurnAborted(_)
         | EventMsg::ShutdownComplete