Adds ai_recipe_generation sample (#2242)

Adding the demo app from my I/O talk. Because AI.

## 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.

---------

Co-authored-by: Brett Morgan <brett.morgan@gmail.com>

ai_recipe_generation/lib/app_bar.dart

@@ -0,0 +1,160 @@
+import 'package:ai_recipe_generation/util/extensions.dart';
+import 'package:flutter/material.dart';
+import 'package:flutter_svg/svg.dart';
+import 'package:material_symbols_icons/symbols.dart';
+
+import 'features/prompt/widgets/app_info_dialog_widget.dart';
+import 'theme.dart';
+import 'widgets/appbar_shape_border.dart';
+
+class AnimatedAppBar extends StatelessWidget {
+  const AnimatedAppBar({
+    super.key,
+    required this.scrollController,
+    required this.textStyle,
+    required this.tabController,
+  });
+
+  final ScrollController scrollController;
+  final double collapsedHeight = 100;
+  final double expandedHeight = 300;
+  final double avatarSize = 50;
+  final TextStyle textStyle;
+  final TabController tabController;
+
+  String get headerText {
+    return switch (tabController.index) {
+      0 => 'Create a recipe',
+      1 => 'Saved recipes',
+      2 => 'Settings',
+      _ => 'Uh oh!',
+    };
+  }
+
+  String get helperText {
+    return switch (tabController.index) {
+      0 =>
+        "Tell me what ingredients you have and what you're feelin', and I'll create a recipe for you!",
+      1 => "These are all my saved recipes created by Chef Noodle.",
+      2 => 'Settings',
+      _ => 'Uh oh!',
+    };
+  }
+
+  @override
+  Widget build(BuildContext context) {
+    return SliverLayoutBuilder(
+      builder: (context, constraints) {
+        return SliverAppBar(
+          automaticallyImplyLeading: false,
+          pinned: true,
+          forceElevated: true,
+          elevation: 2,
+          shadowColor: Colors.black,
+          expandedHeight: expandedHeight,
+          collapsedHeight: collapsedHeight,
+          backgroundColor: Theme.of(context).primaryColor,
+          shape: const AppBarShapeBorder(50),
+          title: Column(
+            children: [
+              Row(
+                crossAxisAlignment: CrossAxisAlignment.center,
+                children: [
+                  SizedBox(
+                    width: avatarSize,
+                    height: avatarSize,
+                    child: SvgPicture.asset(
+                      'assets/chef_cat.svg',
+                      semanticsLabel: 'Chef cat icon',
+                    ),
+                  ),
+                  const SizedBox(
+                    width: MarketplaceTheme.spacing1,
+                  ),
+                  if (scrollController.positions.isNotEmpty &&
+                      scrollController.offset < 200)
+                    Text(
+                      "Meowdy! Let's get cooking!",
+                      style: MarketplaceTheme.heading3,
+                    ),
+                  if (scrollController.positions.isNotEmpty &&
+                      scrollController.offset > 200)
+                    Text(
+                      headerText,
+                      style: MarketplaceTheme.heading3,
+                    ),
+                  const Spacer(),
+                  if (scrollController.positions.isNotEmpty &&
+                      scrollController.offset > 200)
+                    IconButton(
+                      onPressed: () => showDialog<Null>(
+                        context: context,
+                        builder: (context) => const AppInfoDialog(),
+                      ),
+                      icon: const Icon(
+                        Symbols.info,
+                        color: Colors.black12,
+                      ),
+                    ),
+                ],
+              ),
+            ],
+          ),
+          flexibleSpace: FlexibleSpaceBar(
+            background: Padding(
+              padding: const EdgeInsets.all(MarketplaceTheme.spacing4),
+              child: SizedBox(
+                width: MediaQuery.of(context).size.width,
+                child: Row(
+                  mainAxisAlignment: MainAxisAlignment.spaceAround,
+                  children: [
+                    Expanded(
+                      child: Text(
+                        helperText,
+                        style: constraints.isMobile
+                            ? MarketplaceTheme.subheading2
+                            : MarketplaceTheme.subheading1,
+                      ),
+                    ),
+                    IconButton(
+                      onPressed: () {
+                        showDialog<Null>(
+                          context: context,
+                          builder: (context) => const AppInfoDialog(),
+                        );
+                      },
+                      icon: const Icon(
+                        Symbols.info,
+                        color: Colors.black12,
+                      ),
+                    ),
+                  ],
+                ),
+              ),
+            ),
+          ),
+          bottom: PreferredSize(
+            preferredSize: const Size(double.infinity, 0),
+            child: Align(
+              alignment: Alignment.centerLeft,
+              child: Padding(
+                padding: EdgeInsets.only(
+                  left: constraints.isMobile
+                      ? MarketplaceTheme.spacing2
+                      : MarketplaceTheme.spacing1,
+                ),
+                child: AnimatedDefaultTextStyle(
+                  duration: const Duration(milliseconds: 0),
+                  style: textStyle,
+                  child: Text(
+                    headerText,
+                  ),
+                ),
+              ),
+            ),
+          ),
+        );
+      },
+    );
+  }
+}