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/tui/src/chatwidget/protocol.rs

@@ -290,8 +290,8 @@ impl ChatWidget {
                 self.on_patch_apply_begin(file_update_changes_to_display(changes));
             }
             item @ ThreadItem::McpToolCall { .. } => self.on_mcp_tool_call_started(item),
-            ThreadItem::WebSearch { id, .. } => {
-                self.on_web_search_begin(id);
+            ThreadItem::WebSearch(item) => {
+                self.on_web_search_begin(item.id);
             }
             ThreadItem::ImageGeneration(_) => {
                 self.on_image_generation_begin();

codex-rs/tui/src/chatwidget/replay.rs

@@ -139,12 +139,13 @@ impl ChatWidget {
                 ..
             } => self.on_mcp_tool_call_started(item),
             item @ ThreadItem::McpToolCall { .. } => self.on_mcp_tool_call_completed(item),
-            ThreadItem::WebSearch { id, query, action } => {
-                self.on_web_search_begin(id.clone());
+            ThreadItem::WebSearch(item) => {
+                self.on_web_search_begin(item.id.clone());
                 self.on_web_search_end(
-                    id,
-                    query,
-                    action.unwrap_or(codex_app_server_protocol::WebSearchAction::Other),
+                    item.id,
+                    item.query,
+                    item.action
+                        .unwrap_or(codex_app_server_protocol::WebSearchAction::Other),
                 );
             }
             ThreadItem::ImageView { id: _, path } => {