Refactor layers example (#83070)

examples/layers/services/isolate.dart

@@ -210,21 +210,14 @@ class IsolateExampleState extends State<StatefulWidget> with SingleTickerProvide
   String _label = 'Start';
   String _result = ' ';
   double _progress = 0.0;
-  late AnimationController _animation;
-  late CalculationManager _calculationManager;
-
-  @override
-  void initState() {
-    super.initState();
-    _animation = AnimationController(
+  late final AnimationController _animation = AnimationController(
     duration: const Duration(milliseconds: 3600),
     vsync: this,
   )..repeat();
-    _calculationManager = CalculationManager(
+  late final CalculationManager _calculationManager = CalculationManager(
     onProgressListener: _handleProgressUpdate,
     onResultListener: _handleResult,
   );
-  }
 
   @override
   void dispose() {

examples/layers/widgets/spinning_square.dart

@@ -12,19 +12,13 @@ class SpinningSquare extends StatefulWidget {
 }
 
 class _SpinningSquareState extends State<SpinningSquare> with SingleTickerProviderStateMixin {
-  late AnimationController _animation;
-
-  @override
-  void initState() {
-    super.initState();
   // We use 3600 milliseconds instead of 1800 milliseconds because 0.0 -> 1.0
   // represents an entire turn of the square whereas in the other examples
   // we used 0.0 -> math.pi, which is only half a turn.
-    _animation = AnimationController(
+  late final AnimationController _animation = AnimationController(
     duration: const Duration(milliseconds: 3600),
     vsync: this,
   )..repeat();
-  }
 
   @override
   void dispose() {