[showModalBottomSheet] fix: showModalBottomSheet does not move along keyboard (#71636)

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

@@ -375,6 +375,8 @@ class _ModalBottomSheetState<T> extends State<_ModalBottomSheet<T>> {
 
     return AnimatedBuilder(
       animation: widget.route!.animation!,
+      child: Padding(
+        padding: MediaQuery.of(context).viewInsets,
         child: BottomSheet(
           animationController: widget.route!._animationController,
           onClosing: () {
@@ -391,6 +393,7 @@ class _ModalBottomSheetState<T> extends State<_ModalBottomSheet<T>> {
           onDragStart: handleDragStart,
           onDragEnd: handleDragEnd,
         ),
+      ),
       builder: (BuildContext context, Widget? child) {
         // Disable the initial animation when accessible navigation is on so
         // that the semantics are added to the tree at the correct time.

packages/flutter/test/material/bottom_sheet_test.dart

@@ -726,6 +726,41 @@ void main() {
 
     expect(retrievedRouteSettings, routeSettings);
   });
+
+  testWidgets('showModalBottomSheet should move along on-screen keyboard',
+          (WidgetTester tester) async {
+    late BuildContext savedContext;
+
+    // Show a keyboard (simulate by space at the bottom of the screen).
+    await tester.pumpWidget(
+      MaterialApp(
+        home: MediaQuery(
+          data: const MediaQueryData(viewInsets: EdgeInsets.only(bottom: 200)),
+          child: Builder(
+            builder: (BuildContext context) {
+              savedContext = context;
+              return Container();
+            },
+          ),
+        ),
+      ),
+    );
+
+    await tester.pump();
+    expect(find.text('BottomSheet'), findsNothing);
+
+    showModalBottomSheet<void>(
+      context: savedContext,
+      builder: (BuildContext context) {
+        return const Text('BottomSheet');
+      },
+    );
+
+    await tester.pumpAndSettle();
+
+    expect(find.text('BottomSheet'), findsOneWidget);
+    expect(tester.getBottomLeft(find.text('BottomSheet')).dy, 600);
+  });
 }
 
 class _TestPage extends StatelessWidget {