Add `next_gen_ui_demo` to samples index (#1824)

web/next_gen_ui_demo

@@ -0,0 +1 @@
+../next_gen_ui_demo

web/samples_index/lib/src/samples.yaml

@@ -653,3 +653,19 @@ samples:
     web: https://flutter-angular.web.app/
     type: sample
 
+  - name: Next Gen UI demo
+    author: Flutter
+    screenshots:
+      - url: images/next_gen_ui_demo.png
+        alt: Next Gen UI demo screenshot
+    source: https://github.com/flutter/samples/tree/main/next_gen_ui_demo
+    description: A sample version of the Next Generation UI codelab for demoing at I/O Connect
+    difficulty: advanced
+    packages: 
+      - flutter_animate
+    platforms:
+      - Windows, macOS, Linux, web, Android, iOS
+    links:
+      - https://codelabs.developers.google.com/codelabs/flutter-next-gen-uis
+    type: sample
+    web: web/next_gen_ui_demo