Dart 3.9 / Flutter 3.35 [first LLM release] (#2714)

I got carried away with Gemini and basically rewrote CI and the release
process for the new LLM reality. This work was largely completed by
Gemini.

- Bump all SDK versions to the current beta (3.9.0-0)
- Run `flutter channel beta`
- Wrote `ci_script.dart` to replace the bash scripts
- Converted repository to pub workspace #2499 
- Added llm.md and release.md
- Added redirect for deprecated Samples Index

## 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 have added sample code updates to the [changelog].
- [x] I updated/added relevant documentation (doc comments with `///`).

veggieseasons/lib/screens/search.dart

@@ -18,7 +18,8 @@ class SearchScreen extends StatefulWidget {
   State<SearchScreen> createState() => _SearchScreenState();
 }
 
-class _SearchScreenState extends State<SearchScreen> with RestorationMixin {
+class _SearchScreenState extends State<SearchScreen>
+    with RestorationMixin {
   final controller = RestorableTextEditingController();
   final focusNode = FocusNode();
   String? terms;
@@ -87,7 +88,11 @@ class _SearchScreenState extends State<SearchScreen> with RestorationMixin {
           );
         } else {
           return Padding(
-            padding: const EdgeInsets.only(left: 16, right: 16, bottom: 24),
+            padding: const EdgeInsets.only(
+              left: 16,
+              right: 16,
+              bottom: 24,
+            ),
             child: VeggieHeadline(veggies[i - 1]),
           );
         }
@@ -106,7 +111,9 @@ class _SearchScreenState extends State<SearchScreen> with RestorationMixin {
         builder: (context) {
           return AnnotatedRegion<SystemUiOverlayStyle>(
             value: SystemUiOverlayStyle(
-              statusBarBrightness: MediaQuery.platformBrightnessOf(context),
+              statusBarBrightness: MediaQuery.platformBrightnessOf(
+                context,
+              ),
             ),
             child: SafeArea(
               bottom: false,