Next Gen UI demo (#1778)

First pass at a Next Generation UI demo app. The UI needs work, feedback
gratefully accepted.

## Pre-launch Checklist

- [x] I read the [Flutter Style Guide] _recently_, and have followed its
advice.
- [x] I signed the [CLA].
- [x] I read the [Contributors Guide].
- [x] I updated/added relevant documentation (doc comments with `///`).
- [x] All existing and new tests are passing.

If you need help, consider asking for advice on the #hackers-devrel
channel on [Discord].

<!-- Links -->
[Flutter Style Guide]:
https://github.com/flutter/flutter/wiki/Style-guide-for-Flutter-repo
[CLA]: https://cla.developers.google.com/
[Discord]: https://github.com/flutter/flutter/wiki/Chat
[Contributors Guide]:
https://github.com/flutter/samples/blob/main/CONTRIBUTING.md

tool/flutter_ci_script_master.sh

@@ -50,6 +50,7 @@ declare -ar PROJECT_NAMES=(
     "material_3_demo"
     # TODO(DomesticMouse): The '!' will have no effect because the receiver can't be null.
     # "navigation_and_routing"
+    "next_gen_ui_demo"
     "place_tracker"
     # TODO: https://github.com/flutter/samples/issues/1765
     # "platform_channels"