Adjust Flutter gallery inclusion in samples index (#2141)

Reorganizes the samples index to deprioritize the gallery in favor of
some recent web demos, particularly the Material 3 demo.

This PR does keep the gallery in the index, as it is no more out of date
than other samples and there are plans to retire this index. It however
updates its demo link to a new Firebase destination that will remain
hosted for posterity.

Closes https://github.com/flutter/samples/issues/2139

web/samples_index/lib/src/samples.yaml

@@ -1,4 +1,57 @@
 samples:
+  - name: Material 3
+    author: Flutter
+    screenshots:
+      - url: images/material_3_components.png
+        alt: Components tab of the Material 3 demo
+      - url: images/material_3_color.png
+        alt: Colors tab of the Material 3 demo
+      - url: images/material_3_typography.png
+        alt: Typography tab of the Material 3 demo
+      - url: images/material_3_elevation.png
+        alt: Elevation tab of the Material 3 demo
+      - url: images/material_3_green.png
+        alt: Elevation tab of the Material 3 demo with seed color of green
+    source: https://github.com/flutter/samples/tree/main/material_3_demo
+    description: >
+      Showcases Material 3 features in the Flutter Material library.
+      These features include updated components, typography, color system and elevation support.
+    difficulty: beginner
+    widgets:
+      - Theme
+      - TextButton
+      - ElevatedButton
+      - OutlinedButton
+      - Text
+      - Card
+      - AppBar
+    packages: [ ]
+    tags: [ "material", "design", "gallery" ]
+    platforms: [ "ios", "android", "web", "windows", "macos", "linux" ]
+    type: demo
+    web: web/material_3_demo
+
+  - name: Rich Text Editor
+    author: Flutter
+    screenshots:
+      - url: images/simple_editor_active.png
+        alt: Advanced text editing with activity
+      - url: images/simple_editor_initial.png
+        alt: Advanced text editing in initial state
+    source: https://github.com/flutter/samples/tree/main/simplistic_editor
+    description: >
+      This is a fancy text editor sample which shows how to consume fine-grain
+      text editing and selection details from the framework's TextEditingDeltas
+      APIs.
+    difficulty: advanced
+    widgets:
+      - TextInput
+    packages: []
+    tags: ["demo", "text"]
+    platforms: ["ios", "android", "web", "windows", "macos", "linux"]
+    type: demo
+    web: web/simplistic_editor
+
   - name: Gallery
     author: Flutter
     screenshots:
@@ -13,7 +66,7 @@ samples:
       - url: images/gallery5.png
         alt: Shrine app screenshot
     source: https://github.com/flutter/gallery
-    web: https://gallery.flutter.dev
+    web: https://flutter-gallery-archive.web.app
     description: >
       A collection of Material Design & Cupertino widgets, behaviors,
       and vignettes implemented with Flutter.
@@ -85,6 +138,24 @@ samples:
     platforms: ['web', 'ios', 'android']
     type: demo
 
+  - name: Web Embedding
+    author: Flutter and Angular
+    screenshots:
+      - url: images/web_embedding1.png
+        alt: A Flutter app embedded in an Angular app
+      - url: images/web_embedding2.png
+        alt: A Flutter app embedded in an Angular app
+    source: https://github.com/flutter/samples/tree/main/web_embedding
+    description: >
+      An example app showing how to embed Flutter in a web application using Angular
+    difficulty: advanced
+    widgets: []
+    packages: []
+    platforms: ['web']
+    tags: ['demo', 'web', 'add-to-app', 'embedding']
+    web: https://flutter-angular.web.app/
+    type: demo
+
   - name: Add to App
     author: Flutter
     screenshots:
@@ -480,63 +551,6 @@ samples:
     tags: ['demo', 'game']
     type: demo
 
-###################
-#### Web Demos ####
-###################
-
-  - name: Rich Text Editor
-    author: Flutter
-    screenshots:
-      - url: images/simple_editor_active.png
-        alt: Advanced text editing with activity
-      - url: images/simple_editor_initial.png
-        alt: Advanced text editing in initial state
-    source: https://github.com/flutter/samples/tree/main/simplistic_editor
-    description: >
-      This is a fancy text editor sample which shows how to consume fine-grain
-      text editing and selection details from the framework's TextEditingDeltas
-      APIs.
-    difficulty: advanced
-    widgets:
-      - TextInput
-    packages: []
-    tags: ["demo", "text"]
-    platforms: ["ios", "android", "web", "windows", "macos", "linux"]
-    type: demo
-    web: web/simplistic_editor
-
-  - name: Material 3
-    author: Flutter
-    screenshots:
-      - url: images/material_3_components.png
-        alt: Components tab of the Material 3 demo
-      - url: images/material_3_color.png
-        alt: Colors tab of the Material 3 demo
-      - url: images/material_3_typography.png
-        alt: Typography tab of the Material 3 demo
-      - url: images/material_3_elevation.png
-        alt: Elevation tab of the Material 3 demo
-      - url: images/material_3_green.png
-        alt: Elevation tab of the Material 3 demo with seed color of green
-    source: https://github.com/flutter/samples/tree/main/material_3_demo
-    description: >
-      Showcases Material 3 features in the Flutter Material library.
-      These features include updated components, typography, color system and elevation support.
-    difficulty: beginner
-    widgets:
-      - Theme
-      - TextButton
-      - ElevatedButton
-      - OutlinedButton
-      - Text
-      - Card
-      - AppBar
-    packages: []
-    tags: ["material", "design"]
-    platforms: ["ios", "android", "web", "windows", "macos", "linux"]
-    type: demo
-    web: web/material_3_demo
-  
   - name: Game Template
     author: Flutter
     screenshots:
@@ -583,21 +597,3 @@ samples:
     tags: ['demo', 'animation']
     web: https://z.flutter.gallery/#/dice
     type: demo
-
-  - name: Web Embedding
-    author: Flutter and Angular
-    screenshots:
-      - url: images/web_embedding1.png
-        alt: A Flutter app embedded in an Angular app
-      - url: images/web_embedding2.png
-        alt: A Flutter app embedded in an Angular app
-    source: https://github.com/flutter/samples/tree/main/web_embedding
-    description: >
-      An example app showing how to embed Flutter in a web application using Angular
-    difficulty: advanced
-    widgets: []
-    packages: []
-    platforms: ['web']
-    tags: ['demo', 'web', 'add-to-app', 'embedding']
-    web: https://flutter-angular.web.app/
-    type: demo