bug(CdkMenuItem): Main menu closes after clicking on a menu item that is a menu

### Is this a regression?

- [ ] Yes, this behavior used to work in the previous version

### The previous version in which this bug was not present was

_No response_

### Description

Clicking on a menu item that is also a menu will close the whole menu, instead of closing only the opened submenu.

### Reproduction

StackBlitz link: https://stackblitz.com/edit/4aortd
Steps to reproduce:
1. Click on `File` button
2. Click on `New` menu item

### Expected Behavior

The submenu for the `New` menu item is closed (or kept open), the menu associated with `File` is kept open (like a `CdkMenuBar` or the menu nested example: https://material.angular.io/components/menu/examples#menu-nested)

### Actual Behavior

The submenu for the `New` menu item is closed and the `File` menu is closed as well.

### Environment

- Angular: 19.0.0
- CDK/Material: 19.0.0
- Browser(s): 131.0.6778.70 (Official Build) (64-bit)
- Operating System (e.g. Windows, macOS, Ubuntu): Windows 10 Pro

リンクされた StackBlitz の再現例から始め、issue に記載されている File > New の操作を行います。Angular CDK のメニュー実装におけるメニュー項目とサブメニューの閉じる動作を追跡し、nested-menu と CdkMenuBar の例を動作の参考として、New を閉じたときに File が開いたままになることを確認します。

索引モデルが issue の本文から書いたものです。