Support web search (#1370)

<!-- This is an auto-generated description by cubic. -->

## Summary by cubic
Adds web search to Dyad Pro chats with a new UI, tag parsing, and a Pro
Mode toggle that wires through to the engine.

- **New Features**
  - Pro Mode toggle: “Web Search” (settings.enableProWebSearch).
  - New custom tags: dyad-web-search, dyad-web-search-result, dyad-read.
- Collapsible Web Search Result UI with in-progress badge and markdown
rendering.
- Engine integration: passes enable_web_search and activates DyadEngine
when web search is on.

<!-- End of auto-generated description by cubic. -->

src/ipc/utils/get_model_client.ts

@@ -86,7 +86,8 @@ export async function getModelClient(
     if (providerConfig.gatewayPrefix != null || dyadEngineUrl) {
       const isEngineEnabled =
         settings.enableProSmartFilesContextMode ||
-        settings.enableProLazyEditsMode;
+        settings.enableProLazyEditsMode ||
+        settings.enableProWebSearch;
       const provider = isEngineEnabled
         ? createDyadEngine({
             apiKey: dyadApiKey,
@@ -100,6 +101,7 @@ export async function getModelClient(
               enableSmartFilesContext: settings.enableProSmartFilesContextMode,
               // Keep in sync with getCurrentValue in ProModeSelector.tsx
               smartContextMode: settings.proSmartContextOption ?? "balanced",
+              enableWebSearch: settings.enableProWebSearch,
             },
             settings,
           })