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/components/chat/DyadWebSearch.tsx

@@ -0,0 +1,31 @@
+import type React from "react";
+import type { ReactNode } from "react";
+import { Globe } from "lucide-react";
+
+interface DyadWebSearchProps {
+  children?: ReactNode;
+  node?: any;
+  query?: string;
+}
+
+export const DyadWebSearch: React.FC<DyadWebSearchProps> = ({
+  children,
+  node: _node,
+  query: queryProp,
+}) => {
+  const query = queryProp || (typeof children === "string" ? children : "");
+
+  return (
+    <div className="bg-(--background-lightest) rounded-lg px-4 py-2 border my-2">
+      <div className="flex items-center justify-between">
+        <div className="flex items-center gap-2">
+          <Globe size={16} className="text-blue-600" />
+          <div className="text-xs text-blue-600 font-medium">Web Search</div>
+        </div>
+      </div>
+      <div className="text-sm italic text-gray-600 dark:text-gray-300 mt-2">
+        {query || children}
+      </div>
+    </div>
+  );
+};