[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/schema/json/ServerNotification.json

@@ -1932,6 +1932,11 @@
     },
     "ItemCompletedNotification": {
       "properties": {
+        "completedAtMs": {
+          "description": "Unix timestamp (in milliseconds) when this item lifecycle completed.",
+          "format": "int64",
+          "type": "integer"
+        },
         "item": {
           "$ref": "#/definitions/ThreadItem"
         },
@@ -1943,6 +1948,7 @@
         }
       },
       "required": [
+        "completedAtMs",
         "item",
         "threadId",
         "turnId"
@@ -2030,6 +2036,11 @@
         "item": {
           "$ref": "#/definitions/ThreadItem"
         },
+        "startedAtMs": {
+          "description": "Unix timestamp (in milliseconds) when this item lifecycle started.",
+          "format": "int64",
+          "type": "integer"
+        },
         "threadId": {
           "type": "string"
         },
@@ -2039,6 +2050,7 @@
       },
       "required": [
         "item",
+        "startedAtMs",
         "threadId",
         "turnId"
       ],
@@ -5896,4 +5908,4 @@
     }
   ],
   "title": "ServerNotification"
-}
+}