Move JSDoc examples to type-checked .examples.ts files

Extract inline code examples from JSDoc comments into companion
`.examples.ts`/`.examples.tsx` files. Examples are now:

- Type-checked by wrapping them in functions
- Referenced via `{@includeCode ./file.examples.ts#regionName}` tags
- Organized using `//#region` and `//#endregion` markers

This keeps the main source files cleaner while ensuring examples
compile correctly. Updated TypeDoc config with `exampleTag: false`
to support title text on `@example` tags.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

src/react/useApp.examples.tsx

@@ -0,0 +1,54 @@
+/**
+ * Type-checked examples for the useApp hook.
+ *
+ * @module
+ */
+
+import { useApp, McpUiToolInputNotificationSchema } from "./index.js";
+
+/**
+ * Example: Register a notification handler in onAppCreated.
+ */
+function useApp_registerHandler() {
+  //#region useApp_registerHandler
+  useApp({
+    appInfo: { name: "MyApp", version: "1.0.0" },
+    capabilities: {},
+    onAppCreated: (app) => {
+      app.setNotificationHandler(
+        McpUiToolInputNotificationSchema,
+        (notification) => {
+          console.log("Tool input:", notification.params.arguments);
+        },
+      );
+    },
+  });
+  //#endregion useApp_registerHandler
+}
+
+/**
+ * Example: Basic usage of useApp hook.
+ */
+function useApp_basicUsage() {
+  //#region useApp_basicUsage
+  function MyApp() {
+    const { app, isConnected, error } = useApp({
+      appInfo: { name: "MyApp", version: "1.0.0" },
+      capabilities: {},
+      onAppCreated: (app) => {
+        // Register handlers before connection
+        app.setNotificationHandler(
+          McpUiToolInputNotificationSchema,
+          (notification) => {
+            console.log("Tool input:", notification.params.arguments);
+          },
+        );
+      },
+    });
+
+    if (error) return <div>Error: {error.message}</div>;
+    if (!isConnected) return <div>Connecting...</div>;
+    return <div>Connected!</div>;
+  }
+  //#endregion useApp_basicUsage
+}