[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)
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* #18748
* #18747
* #17090
* #17089
* __->__ #20514

codex-rs/protocol/src/dynamic_tools.rs

@@ -23,6 +23,8 @@ pub struct DynamicToolCallRequest {
     pub call_id: String,
     pub turn_id: String,
     #[serde(default)]
+    pub started_at_ms: i64,
+    #[serde(default)]
     pub namespace: Option<String>,
     pub tool: String,
     pub arguments: JsonValue,