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

next_gen_ui_demo/windows/runner/flutter_window.cpp

@@ -0,0 +1,66 @@
+#include "flutter_window.h"
+
+#include <optional>
+
+#include "flutter/generated_plugin_registrant.h"
+
+FlutterWindow::FlutterWindow(const flutter::DartProject& project)
+    : project_(project) {}
+
+FlutterWindow::~FlutterWindow() {}
+
+bool FlutterWindow::OnCreate() {
+  if (!Win32Window::OnCreate()) {
+    return false;
+  }
+
+  RECT frame = GetClientArea();
+
+  // The size here must match the window dimensions to avoid unnecessary surface
+  // creation / destruction in the startup path.
+  flutter_controller_ = std::make_unique<flutter::FlutterViewController>(
+      frame.right - frame.left, frame.bottom - frame.top, project_);
+  // Ensure that basic setup of the controller was successful.
+  if (!flutter_controller_->engine() || !flutter_controller_->view()) {
+    return false;
+  }
+  RegisterPlugins(flutter_controller_->engine());
+  SetChildContent(flutter_controller_->view()->GetNativeWindow());
+
+  flutter_controller_->engine()->SetNextFrameCallback([&]() {
+    this->Show();
+  });
+
+  return true;
+}
+
+void FlutterWindow::OnDestroy() {
+  if (flutter_controller_) {
+    flutter_controller_ = nullptr;
+  }
+
+  Win32Window::OnDestroy();
+}
+
+LRESULT
+FlutterWindow::MessageHandler(HWND hwnd, UINT const message,
+                              WPARAM const wparam,
+                              LPARAM const lparam) noexcept {
+  // Give Flutter, including plugins, an opportunity to handle window messages.
+  if (flutter_controller_) {
+    std::optional<LRESULT> result =
+        flutter_controller_->HandleTopLevelWindowProc(hwnd, message, wparam,
+                                                      lparam);
+    if (result) {
+      return *result;
+    }
+  }
+
+  switch (message) {
+    case WM_FONTCHANGE:
+      flutter_controller_->engine()->ReloadSystemFonts();
+      break;
+  }
+
+  return Win32Window::MessageHandler(hwnd, message, wparam, lparam);
+}