[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/exec/src/event_processor_with_jsonl_output_tests.rs

@@ -20,6 +20,7 @@ fn failed_turn_does_not_overwrite_output_last_message_file() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
         },
     ));
 

codex-rs/exec/tests/event_processor_with_json_output.rs

@@ -181,6 +181,7 @@ fn command_execution_started_and_completed_translate_to_thread_events() {
             item: command_item,
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            started_at_ms: 0,
         }));
     assert_eq!(
         started,
@@ -216,6 +217,7 @@ fn command_execution_started_and_completed_translate_to_thread_events() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
         },
     ));
     assert_eq!(
@@ -250,6 +252,7 @@ fn empty_reasoning_items_are_ignored() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
         },
     ));
 
@@ -274,6 +277,7 @@ fn unsupported_items_do_not_consume_synthetic_ids() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
         },
     ));
 
@@ -295,6 +299,7 @@ fn unsupported_items_do_not_consume_synthetic_ids() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
         },
     ));
 
@@ -327,6 +332,7 @@ fn reasoning_items_emit_summary_not_raw_content() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
         },
     ));
 
@@ -362,6 +368,7 @@ fn web_search_completion_preserves_query_and_action() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
         },
     ));
 
@@ -399,6 +406,7 @@ fn web_search_start_and_completion_reuse_item_id() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            started_at_ms: 0,
         }));
 
     let completed = processor.collect_thread_events(ServerNotification::ItemCompleted(
@@ -413,6 +421,7 @@ fn web_search_start_and_completion_reuse_item_id() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
         },
     ));
 
@@ -472,6 +481,7 @@ fn mcp_tool_call_begin_and_end_emit_item_events() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            started_at_ms: 0,
         }));
     let completed = processor.collect_thread_events(ServerNotification::ItemCompleted(
         ItemCompletedNotification {
@@ -492,6 +502,7 @@ fn mcp_tool_call_begin_and_end_emit_item_events() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
         },
     ));
 
@@ -559,6 +570,7 @@ fn mcp_tool_call_failure_sets_failed_status() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
         },
     ));
 
@@ -604,6 +616,7 @@ fn mcp_tool_call_defaults_arguments_and_preserves_structured_content() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            started_at_ms: 0,
         }));
     let completed = processor.collect_thread_events(ServerNotification::ItemCompleted(
         ItemCompletedNotification {
@@ -627,6 +640,7 @@ fn mcp_tool_call_defaults_arguments_and_preserves_structured_content() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
         },
     ));
 
@@ -695,6 +709,7 @@ fn collab_spawn_begin_and_end_emit_item_events() {
             },
             thread_id: "thread-parent".to_string(),
             turn_id: "turn-1".to_string(),
+            started_at_ms: 0,
         }));
     let completed = processor.collect_thread_events(ServerNotification::ItemCompleted(
         ItemCompletedNotification {
@@ -717,6 +732,7 @@ fn collab_spawn_begin_and_end_emit_item_events() {
             },
             thread_id: "thread-parent".to_string(),
             turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
         },
     ));
 
@@ -795,6 +811,7 @@ fn file_change_completion_maps_change_kinds() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
         },
     ));
 
@@ -845,6 +862,7 @@ fn file_change_declined_maps_to_failed_status() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
         },
     ));
 
@@ -882,6 +900,7 @@ fn agent_message_item_updates_final_message() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
         },
     ));
 
@@ -916,6 +935,7 @@ fn agent_message_item_started_is_ignored() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            started_at_ms: 0,
         }));
 
     assert_eq!(
@@ -940,6 +960,7 @@ fn reasoning_item_completed_uses_synthetic_id() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
         },
     ));
 
@@ -1296,6 +1317,7 @@ fn turn_completion_reconciles_started_items_from_turn_items() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            started_at_ms: 0,
         }));
     assert_eq!(
         started,
@@ -1378,6 +1400,7 @@ fn turn_completion_overwrites_stale_final_message_from_turn_items() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
         },
     ));
 
@@ -1426,6 +1449,7 @@ fn turn_completion_preserves_streamed_final_message_when_turn_items_are_empty()
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
         },
     ));
 
@@ -1470,6 +1494,7 @@ fn failed_turn_clears_stale_final_message() {
             },
             thread_id: "thread-1".to_string(),
             turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
         },
     ));