bug(MatGroupTabs): MatTabBody content within a MatMenu does not display

### 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

MatTab content in a mat menu will disappear when opening and closing the menu and transitioning between tabs. I believe the animations set the visibility to hidden; however, it will get in a state where it thinks it should be hidden even though the tab is highlighted causing the tab label to be the only thing visible.

### Reproduction

StackBlitz link: https://stackblitz.com/edit/ewu1na?file=src%2Fexample%2Fmenu-overview-example.html
Steps to reproduce:
1. Open Mat Menu
2. Select Second Tab
3. Click outside of MatMenu to close menu
4. Open menu and rapidly select either tab (may have to repeat steps 1-4). The key is to rapidly click the tabs, the content will disappear and will not come back until a few transitions. I think the animation is hiding it and never triggering it to display

### Expected Behavior

I expect tab content to be visible when a tab is in view and selected.

### Actual Behavior

Tab content is hidden tab content should be visible

### Environment

- Angular: 16.03
- CDK/Material: 16
- Browser(s): Edge
- Operating System (e.g. Windows, macOS, Ubuntu): Windows

リンクされた StackBlitz の再現から始め、タブをすばやく切り替えてメニューを再度開く際の MatMenu 内部における MatGroupTabs/MatTabBody の動作を追跡します。選択されたタブのコンテンツが非表示のままになる遷移状態を調査します。繰り返しメニューを閉じ、再度開き、タブを切り替えるサイクルの後も選択されたコンテンツが表示されたままになれば完了です。

索引モデルが issue の本文から書いたものです。