[DropdownMenu] Close menu after editing is complete (#130710)

Fixes: #130674 

Before: The dropdown menu was not closed if empty text was provided

After: The dropdown menu is closed even if empty text is provided

https://github.com/flutter/flutter/assets/61322712/fccac501-9fca-4f60-8a94-abfc50552ec9

*If you had to change anything in the [flutter/tests] repo, include a link to the migration guide as per the [breaking change policy].*

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

@@ -612,9 +612,7 @@ class _DropdownMenuState<T> extends State<DropdownMenu<T>> {
               if (!widget.enableSearch) {
                 currentHighlight = null;
               }
-              if (_textEditingController.text.isNotEmpty) {
+              controller.close();
-                controller.close();
-              }
             },
             onTap: () {
               handlePressed(controller);

packages/flutter/test/material/dropdown_menu_test.dart

@@ -1050,6 +1050,34 @@ void main() {
     expect(controller.text, 'New Item');
   });
 
+  testWidgets('The menu should be closed after text editing is complete', (WidgetTester tester) async {
+    final ThemeData themeData = ThemeData();
+    final TextEditingController controller = TextEditingController();
+    await tester.pumpWidget(MaterialApp(
+      theme: themeData,
+      home: Scaffold(
+        body: DropdownMenu<TestMenu>(
+          requestFocusOnTap: true,
+          enableFilter: true,
+          dropdownMenuEntries: menuChildren,
+          controller: controller,
+        ),
+      ),
+    ));
+    // Access the MenuAnchor
+    final MenuAnchor menuAnchor = tester.widget<MenuAnchor>(find.byType(MenuAnchor));
+
+    // Open the menu
+    await tester.tap(find.byType(DropdownMenu<TestMenu>));
+    await tester.pumpAndSettle();
+    expect(menuAnchor.controller!.isOpen, true);
+
+    // Simulate `TextInputAction.done` on textfield
+    await tester.testTextInput.receiveAction(TextInputAction.done);
+    await tester.pumpAndSettle();
+    expect(menuAnchor.controller!.isOpen, false);
+  });
+
   testWidgets('The onSelected gets called only when a selection is made', (WidgetTester tester) async {
     int selectionCount = 0;