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-trace/src/protocol_event.rs

@@ -260,7 +260,6 @@ pub(crate) fn tool_runtime_trace_event(event: &EventMsg) -> Option<ToolRuntimeTr
         | EventMsg::PatchApplyUpdated(_)
         | EventMsg::TurnDiff(_)
         | EventMsg::RealtimeConversationListVoicesResponse(_)
-        | EventMsg::SkillsUpdateAvailable
         | EventMsg::PlanUpdate(_)
         | EventMsg::TurnAborted(_)
         | EventMsg::ShutdownComplete
@@ -333,7 +332,6 @@ pub(crate) fn wrapped_protocol_event_type(event: &EventMsg) -> Option<&'static s
         | EventMsg::PatchApplyEnd(_)
         | EventMsg::TurnDiff(_)
         | EventMsg::RealtimeConversationListVoicesResponse(_)
-        | EventMsg::SkillsUpdateAvailable
         | EventMsg::PlanUpdate(_)
         | EventMsg::EnteredReviewMode(_)
         | EventMsg::ExitedReviewMode(_)