Extract getUiCapability example to type-checked examples file

Move the inline example from the `getUiCapability()` JSDoc to
`index.examples.ts` for type checking, following the pattern used
by other examples in the codebase.

The example now uses the correct MCP SDK API:
- `server.server.oninitialized` callback for post-initialization hook
- `server.server.getClientCapabilities()` to retrieve capabilities

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

src/server/index.examples.ts

@@ -17,6 +17,7 @@ import { z } from "zod";
 import {
   registerAppTool,
   registerAppResource,
+  getUiCapability,
   RESOURCE_MIME_TYPE,
 } from "./index.js";
 
@@ -196,3 +197,41 @@ function registerAppResource_withCsp(
   );
   //#endregion registerAppResource_withCsp
 }
+
+/**
+ * Example: Check for MCP Apps support in server initialization.
+ */
+function getUiCapability_checkSupport(
+  server: McpServer,
+  weatherHandler: ToolCallback,
+  textWeatherHandler: ToolCallback,
+) {
+  //#region getUiCapability_checkSupport
+  server.server.oninitialized = () => {
+    const clientCapabilities = server.server.getClientCapabilities();
+    const uiCap = getUiCapability(clientCapabilities);
+
+    if (uiCap?.mimeTypes?.includes(RESOURCE_MIME_TYPE)) {
+      // App-enhanced tool
+      registerAppTool(
+        server,
+        "weather",
+        {
+          description: "Get weather information with interactive dashboard",
+          _meta: { ui: { resourceUri: "ui://weather/dashboard" } },
+        },
+        weatherHandler,
+      );
+    } else {
+      // Text-only fallback
+      server.registerTool(
+        "weather",
+        {
+          description: "Get weather information",
+        },
+        textWeatherHandler,
+      );
+    }
+  };
+  //#endregion getUiCapability_checkSupport
+}