`AppBar`: Fix nested scroll view doesn't update `AppBar` elevation for Material 3 (#103899)

packages/flutter/lib/src/material/app_bar.dart

@@ -162,6 +162,7 @@ class AppBar extends StatefulWidget implements PreferredSizeWidget {
     this.bottom,
     this.elevation,
     this.scrolledUnderElevation,
+    this.notificationPredicate = defaultScrollNotificationPredicate,
     this.shadowColor,
     this.surfaceTintColor,
     this.shape,
@@ -197,6 +198,7 @@ class AppBar extends StatefulWidget implements PreferredSizeWidget {
     this.systemOverlayStyle,
   }) : assert(automaticallyImplyLeading != null),
        assert(elevation == null || elevation >= 0.0),
+       assert(notificationPredicate != null),
        assert(primary != null),
        assert(toolbarOpacity != null),
        assert(bottomOpacity != null),
@@ -421,6 +423,13 @@ class AppBar extends StatefulWidget implements PreferredSizeWidget {
   ///    shadow.
   final double? scrolledUnderElevation;
 
+  /// A check that specifies which child's [ScrollNotification]s should be
+  /// listened to.
+  ///
+  /// By default, checks whether `notification.depth == 0`. Set it to something
+  /// else for more complicated layouts.
+  final ScrollNotificationPredicate notificationPredicate;
+
   /// {@template flutter.material.appbar.shadowColor}
   /// The color of the shadow below the app bar.
   ///
@@ -809,7 +818,7 @@ class _AppBarState extends State<AppBar> {
   }
 
   void _handleScrollNotification(ScrollNotification notification) {
-    if (notification is ScrollUpdateNotification && notification.depth == 0) {
+    if (notification is ScrollUpdateNotification && widget.notificationPredicate(notification)) {
       final bool oldScrolledUnder = _scrolledUnder;
       final ScrollMetrics metrics = notification.metrics;
       switch (metrics.axisDirection) {

packages/flutter/test/material/app_bar_test.dart

@@ -1011,6 +1011,53 @@ void main() {
     expect(getMaterial().elevation, 10);
   });
 
+  testWidgets('scrolledUnderElevation with nested scroll view', (WidgetTester tester) async {
+    Widget buildAppBar({double? scrolledUnderElevation}) {
+      return MaterialApp(
+        theme: ThemeData(useMaterial3: true),
+        home: Scaffold(
+          appBar: AppBar(
+            title: const Text('Title'),
+            scrolledUnderElevation: scrolledUnderElevation,
+            notificationPredicate: (ScrollNotification notification) {
+              return notification.depth == 1;
+            },
+          ),
+          body: ListView.builder(
+            scrollDirection: Axis.horizontal,
+            itemCount: 4,
+            itemBuilder: (BuildContext context, int index) {
+              return SizedBox(
+                height: 600.0,
+                width: 800.0,
+                child: ListView.builder(
+                  itemCount: 100,
+                  itemBuilder: (BuildContext context, int index) =>
+                    ListTile(title: Text('Item $index')),
+                ),
+              );
+            },
+          ),
+        ),
+      );
+    }
+
+    Material getMaterial() => tester.widget<Material>(find.descendant(
+      of: find.byType(AppBar),
+      matching: find.byType(Material),
+    ));
+
+    await tester.pumpWidget(buildAppBar(scrolledUnderElevation: 10));
+    // Starts with the base elevation.
+    expect(getMaterial().elevation, 0.0);
+
+    await tester.fling(find.text('Item 2'), const Offset(0.0, -600.0), 2000.0);
+    await tester.pumpAndSettle();
+
+    // After scrolling it should be the scrolledUnderElevation.
+    expect(getMaterial().elevation, 10);
+  });
+
   group('SliverAppBar elevation', () {
     Widget buildSliverAppBar(bool forceElevated, {double? elevation, double? themeElevation}) {
       return MaterialApp(