[codex-analytics] add item lifecycle timing (#20514)

## Why

Tool families already disagree on what their existing `duration` fields
mean, so lifecycle latency should live on the shared item envelope
instead of being inferred from per-tool execution fields. Carrying that
envelope through app-server notifications gives downstream consumers one
reusable timing signal without pretending every tool has the same
execution semantics.

## What changed

- Adds `started_at_ms` to core `ItemStartedEvent` values and
`completed_at_ms` to core `ItemCompletedEvent` values.
- Populates those timestamps in the shared session lifecycle emitters,
so protocol-native items get timing without each producer tracking its
own clock state.
- Exposes `startedAtMs` on app-server `item/started` notifications and
`completedAtMs` on `item/completed` notifications.
- Maps the lifecycle timestamps through the app-server boundary while
leaving legacy-converted notifications nullable when no lifecycle
timestamp exists.
- Regenerates the app-server JSON schema and TypeScript fixtures for the
notification-envelope change and updates downstream fixtures that
construct those notifications directly.
- Extends the existing web-search and image-generation integration flows
to assert the new lifecycle timestamps on the native item events.

## Verification

- `cargo check -p codex-protocol -p codex-core -p
codex-app-server-protocol -p codex-app-server -p codex-tui -p codex-exec
-p codex-app-server-client`
- `cargo test -p codex-core --test all web_search_item_is_emitted`
- `cargo test -p codex-core --test all
image_generation_call_event_is_emitted`
- `cargo test -p codex-app-server-protocol`

---
[//]: # (BEGIN SAPLING FOOTER)
Stack created with [Sapling](https://sapling-scm.com). Best reviewed
with [ReviewStack](https://reviewstack.dev/openai/codex/pull/20514).
* #18748
* #18747
* #17090
* #17089
* __->__ #20514

codex-rs/app-server-protocol/src/protocol/event_mapping.rs

@@ -69,6 +69,7 @@ pub fn item_event_to_server_notification(
                 thread_id,
                 turn_id: response.turn_id,
                 item,
+                completed_at_ms: response.completed_at_ms,
             })
         }
         EventMsg::CollabAgentSpawnBegin(begin_event) => {
@@ -87,6 +88,7 @@ pub fn item_event_to_server_notification(
                 thread_id,
                 turn_id,
                 item,
+                started_at_ms: begin_event.started_at_ms,
             })
         }
         EventMsg::CollabAgentSpawnEnd(end_event) => {
@@ -125,6 +127,7 @@ pub fn item_event_to_server_notification(
                 thread_id,
                 turn_id,
                 item,
+                completed_at_ms: end_event.completed_at_ms,
             })
         }
         EventMsg::CollabAgentInteractionBegin(begin_event) => {
@@ -144,6 +147,7 @@ pub fn item_event_to_server_notification(
                 thread_id,
                 turn_id,
                 item,
+                started_at_ms: begin_event.started_at_ms,
             })
         }
         EventMsg::CollabAgentInteractionEnd(end_event) => {
@@ -171,6 +175,7 @@ pub fn item_event_to_server_notification(
                 thread_id,
                 turn_id,
                 item,
+                completed_at_ms: end_event.completed_at_ms,
             })
         }
         EventMsg::CollabWaitingBegin(begin_event) => {
@@ -194,6 +199,7 @@ pub fn item_event_to_server_notification(
                 thread_id,
                 turn_id,
                 item,
+                started_at_ms: begin_event.started_at_ms,
             })
         }
         EventMsg::CollabWaitingEnd(end_event) => {
@@ -229,6 +235,7 @@ pub fn item_event_to_server_notification(
                 thread_id,
                 turn_id,
                 item,
+                completed_at_ms: end_event.completed_at_ms,
             })
         }
         EventMsg::CollabCloseBegin(begin_event) => {
@@ -247,6 +254,7 @@ pub fn item_event_to_server_notification(
                 thread_id,
                 turn_id,
                 item,
+                started_at_ms: begin_event.started_at_ms,
             })
         }
         EventMsg::CollabCloseEnd(end_event) => {
@@ -279,6 +287,7 @@ pub fn item_event_to_server_notification(
                 thread_id,
                 turn_id,
                 item,
+                completed_at_ms: end_event.completed_at_ms,
             })
         }
         EventMsg::CollabResumeBegin(begin_event) => {
@@ -297,6 +306,7 @@ pub fn item_event_to_server_notification(
                 thread_id,
                 turn_id,
                 item,
+                started_at_ms: begin_event.started_at_ms,
             })
         }
         EventMsg::CollabResumeEnd(end_event) => {
@@ -329,6 +339,7 @@ pub fn item_event_to_server_notification(
                 thread_id,
                 turn_id,
                 item,
+                completed_at_ms: end_event.completed_at_ms,
             })
         }
         EventMsg::AgentMessageContentDelta(event) => {
@@ -378,6 +389,7 @@ pub fn item_event_to_server_notification(
                 thread_id,
                 turn_id,
                 item: item_started_event.item.into(),
+                started_at_ms: item_started_event.started_at_ms,
             })
         }
         EventMsg::ItemCompleted(item_completed_event) => {
@@ -385,6 +397,7 @@ pub fn item_event_to_server_notification(
                 thread_id,
                 turn_id,
                 item: item_completed_event.item.into(),
+                completed_at_ms: item_completed_event.completed_at_ms,
             })
         }
         EventMsg::PatchApplyUpdated(event) => {
@@ -400,6 +413,7 @@ pub fn item_event_to_server_notification(
                 thread_id,
                 turn_id,
                 item: build_command_execution_begin_item(&exec_command_begin_event),
+                started_at_ms: exec_command_begin_event.started_at_ms,
             })
         }
         EventMsg::ExecCommandOutputDelta(exec_command_output_delta_event) => {
@@ -428,6 +442,7 @@ pub fn item_event_to_server_notification(
                 thread_id,
                 turn_id,
                 item: build_command_execution_end_item(&exec_command_end_event),
+                completed_at_ms: exec_command_end_event.completed_at_ms,
             })
         }
         _ => unreachable!("unsupported item event"),
@@ -480,6 +495,7 @@ mod tests {
     fn collab_resume_begin_maps_to_item_started_resume_agent() {
         let event = CollabResumeBeginEvent {
             call_id: "call-1".to_string(),
+            started_at_ms: 123,
             sender_thread_id: ThreadId::new(),
             receiver_thread_id: ThreadId::new(),
             receiver_agent_nickname: None,
@@ -496,6 +512,7 @@ mod tests {
             ItemStartedNotification {
                 thread_id: "thread-1".to_string(),
                 turn_id: "turn-1".to_string(),
+                started_at_ms: event.started_at_ms,
                 item: ThreadItem::CollabAgentToolCall {
                     id: event.call_id,
                     tool: CollabAgentTool::ResumeAgent,
@@ -515,6 +532,7 @@ mod tests {
     fn collab_resume_end_maps_to_item_completed_resume_agent() {
         let event = CollabResumeEndEvent {
             call_id: "call-2".to_string(),
+            completed_at_ms: 456,
             sender_thread_id: ThreadId::new(),
             receiver_thread_id: ThreadId::new(),
             receiver_agent_nickname: None,
@@ -533,6 +551,7 @@ mod tests {
             ItemCompletedNotification {
                 thread_id: "thread-2".to_string(),
                 turn_id: "turn-2".to_string(),
+                completed_at_ms: event.completed_at_ms,
                 item: ThreadItem::CollabAgentToolCall {
                     id: event.call_id,
                     tool: CollabAgentTool::ResumeAgent,