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 `///`).

animations/test/misc/carousel_test.dart

@@ -18,7 +18,11 @@ void main() {
       expect(imageList.length, 2);
 
       // Swipe the Carousel.
-      await tester.fling(find.byType(CarouselDemo), const Offset(-400, 0), 800);
+      await tester.fling(
+        find.byType(CarouselDemo),
+        const Offset(-400, 0),
+        800,
+      );
       await tester.pumpAndSettle();
 
       // Get the images available on the screen after swipe.