[codex] Add interruptible sleep tool (#28429)

## Why

Models sometimes need to pause briefly while waiting for external work,
but using a shell command for that delay ties the wait to a process and
does not naturally resume when new turn input arrives.

## What changed

- add a built-in `sleep` tool behind the under-development `sleep_tool`
feature
- accept a bounded `duration_ms` argument, matching the millisecond
convention used by unified exec
- end the sleep early when either steered user input or mailbox input
arrives
- include elapsed wall-clock time in completed and interrupted outputs
- emit a dedicated core `SleepItem` through `item/started` and
`item/completed`
- expose the sleep item as app-server v2 `ThreadItem::Sleep` and retain
it in reconstructed thread history
- regenerate the configuration schema for the new feature flag
- regenerate app-server JSON and TypeScript schema fixtures

## Test plan

- `just test -p codex-core sleep_tool_follows_feature_gate`
- `just test -p codex-core any_new_input_interrupts_sleep`
- `just test -p codex-app-server-protocol`
- `just test -p codex-app-server
sleep_emits_started_and_completed_items`

codex-rs/tui/src/app/agent_status_feed.rs

@@ -188,7 +188,9 @@ fn activity_summary(item: &ThreadItem) -> Option<String> {
         ThreadItem::EnteredReviewMode { .. } => return Some("Entered review mode".to_string()),
         ThreadItem::ExitedReviewMode { .. } => return Some("Exited review mode".to_string()),
         ThreadItem::ContextCompaction { .. } => return Some("Compacted context".to_string()),
-        ThreadItem::UserMessage { .. } | ThreadItem::HookPrompt { .. } => return None,
+        ThreadItem::UserMessage { .. }
+        | ThreadItem::HookPrompt { .. }
+        | ThreadItem::Sleep { .. } => return None,
     };
     bounded_summary(summary)
 }

codex-rs/tui/src/chatwidget/replay.rs

@@ -193,6 +193,7 @@ impl ChatWidget {
             }),
             item @ ThreadItem::SubAgentActivity { .. } => self.on_sub_agent_activity(item),
             ThreadItem::DynamicToolCall { .. } => {}
+            ThreadItem::Sleep { .. } => {}
         }
 
         if matches!(replay_kind, Some(ReplayKind::ThreadSnapshot)) && turn_id.is_empty() {

codex-rs/tui/src/thread_transcript.rs

@@ -226,7 +226,8 @@ fn fallback_transcript_cell(item: &ThreadItem) -> Option<PlainHistoryCell> {
         ThreadItem::UserMessage { .. }
         | ThreadItem::AgentMessage { .. }
         | ThreadItem::Plan { .. }
-        | ThreadItem::Reasoning { .. } => return None,
+        | ThreadItem::Reasoning { .. }
+        | ThreadItem::Sleep { .. } => return None,
     };
     (!lines.is_empty()).then(|| PlainHistoryCell::new(lines))
 }