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/app-server-protocol/src/protocol/v2/tests.rs

@@ -19,7 +19,7 @@ use codex_protocol::items::ReasoningItem;
 use codex_protocol::items::SubAgentActivityItem;
 use codex_protocol::items::TurnItem;
 use codex_protocol::items::UserMessageItem;
-use codex_protocol::items::WebSearchItem;
+use codex_protocol::items::WebSearchItem as CoreWebSearchItem;
 use codex_protocol::mcp::CallToolResult;
 use codex_protocol::mcp::McpServerInfo;
 use codex_protocol::memory_citation::MemoryCitation as CoreMemoryCitation;
@@ -2770,7 +2770,7 @@ fn core_turn_item_into_thread_item_converts_supported_variants() {
         }
     );
 
-    let search_item = TurnItem::WebSearch(WebSearchItem {
+    let search_item = TurnItem::WebSearch(CoreWebSearchItem {
         id: "search-1".to_string(),
         query: "docs".to_string(),
         action: CoreWebSearchAction::Search {
@@ -2779,16 +2779,24 @@ fn core_turn_item_into_thread_item_converts_supported_variants() {
         },
     });
 
+    let expected_search_item = WebSearchItem {
+        id: "search-1".to_string(),
+        query: "docs".to_string(),
+        action: Some(WebSearchAction::Search {
+            query: Some("docs".to_string()),
+            queries: None,
+        }),
+    };
+
     assert_eq!(
         ThreadItem::from(search_item),
-        ThreadItem::WebSearch {
-            id: "search-1".to_string(),
-            query: "docs".to_string(),
-            action: Some(WebSearchAction::Search {
-                query: Some("docs".to_string()),
-                queries: None,
-            }),
-        }
+        ThreadItem::WebSearch(expected_search_item.clone())
+    );
+    assert_eq!(
+        ThreadItem::from(TurnItem::Extension(
+            codex_extension_items::ExtensionItem::WebSearch(expected_search_item.clone()),
+        )),
+        ThreadItem::WebSearch(expected_search_item)
     );
 
     let image_view_item = TurnItem::ImageView(ImageViewItem {