core: migrate standalone web search to extension-owned turn items (#31525)

## Description

This PR migrates standalone web search onto the extension-owned
turn-item path introduced in #31283.

Standalone web search now emits `ExtensionItem::WebSearch` through
generic `TurnItem::Extension`, while app-server still exposes the
existing typed `ThreadItem::WebSearch` JSON shape. Hosted Responses API
web search stays on core-owned `TurnItem::WebSearch`.

## What changed

- Added `web_search::WebSearchItem` and `WebSearchAction` to
`codex-extension-items` under the stable `web.search` kind.
- Collapsed `ExtensionTurnItem` to generic `{ item, legacy_events }` now
that no typed extension special cases remain.
- Kept the existing `WebSearchBegin` / `WebSearchEnd` compatibility
events and canonical-first ordering.
- Updated app-server projection/history and generated TypeScript; the
app-server JSON schema is unchanged.

codex-rs/ext/image-generation/src/tool.rs

@@ -101,7 +101,7 @@ fn legacy_end_event(item: &ImageGenerationItem) -> EventMsg {
 }
 
 fn extension_turn_item(item: ImageGenerationItem, legacy_event: EventMsg) -> ExtensionTurnItem {
-    ExtensionTurnItem::Extension {
+    ExtensionTurnItem {
         item: ExtensionItem::ImageGeneration(item),
         legacy_events: vec![legacy_event],
     }