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/rollout/src/policy.rs

@@ -169,7 +169,6 @@ fn event_msg_persistence_mode(ev: &EventMsg) -> Option<EventPersistenceMode> {
         | EventMsg::ReasoningContentDelta(_)
         | EventMsg::ReasoningRawContentDelta(_)
         | EventMsg::ImageGenerationBegin(_)
-        | EventMsg::SkillsUpdateAvailable
         | EventMsg::CollabAgentSpawnBegin(_)
         | EventMsg::CollabAgentInteractionBegin(_)
         | EventMsg::CollabWaitingBegin(_)