Add DropdownMenu.restorationId (#166684)

## Description

This PR introduces `DropdownMenu.restorationId`.
This value is passed to the inner `TextField.restorationId` which is
required to activate the TextField restoration capability.

## Related Issue

Required for https://github.com/flutter/flutter/pull/163721

## Tests

Adds 1 test.

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

diff --git a/packages/flutter/lib/src/material/dropdown_menu.dart b/packages/flutter/lib/src/material/dropdown_menu.dart
index 52326b9..1d8c0f0 100644
--- a/packages/flutter/lib/src/material/dropdown_menu.dart
+++ b/packages/flutter/lib/src/material/dropdown_menu.dart
@@ -190,6 +190,7 @@
     this.closeBehavior = DropdownMenuCloseBehavior.all,
     this.maxLines = 1,
     this.textInputAction,
+    this.restorationId,
   }) : assert(filterCallback == null || enableFilter);
 
   /// Determine if the [DropdownMenu] is enabled.
@@ -527,6 +528,9 @@
   /// {@macro flutter.widgets.TextField.textInputAction}
   final TextInputAction? textInputAction;
 
+  /// {@macro flutter.material.textfield.restorationId}
+  final String? restorationId;
+
   @override
   State<DropdownMenu<T>> createState() => _DropdownMenuState<T>();
 }
@@ -1070,6 +1074,7 @@
                     : null,
             suffixIcon: trailingButton,
           ).applyDefaults(effectiveInputDecorationTheme),
+          restorationId: widget.restorationId,
         );
 
         // If [expandedInsets] is not null, the width of the text field should depend

packages/flutter/test/material/dropdown_menu_test.dart

diff --git a/packages/flutter/test/material/dropdown_menu_test.dart b/packages/flutter/test/material/dropdown_menu_test.dart
index 99123f4..073230a 100644
--- a/packages/flutter/test/material/dropdown_menu_test.dart
+++ b/packages/flutter/test/material/dropdown_menu_test.dart
@@ -4213,6 +4213,27 @@
 
     semantics.dispose();
   });
+
+  testWidgets('restorationId is passed to inner TextField', (WidgetTester tester) async {
+    const String restorationId = 'dropdown_menu';
+
+    await tester.pumpWidget(
+      MaterialApp(
+        home: Scaffold(
+          body: DropdownMenu<TestMenu>(
+            dropdownMenuEntries: menuChildren,
+            requestFocusOnTap: true,
+            restorationId: restorationId,
+          ),
+        ),
+      ),
+    );
+
+    expect(find.byType(TextField), findsOne);
+
+    final TextField textField = tester.firstWidget(find.byType(TextField));
+    expect(textField.restorationId, restorationId);
+  });
 }
 
 enum TestMenu {