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

Start with the linked StackBlitz reproduction and follow the MatGroupTabs/MatTabBody behavior inside MatMenu while rapidly switching tabs and reopening the menu. Investigate the transition state that leaves selected tab content hidden; done means selected content remains visible after repeated close, reopen, and tab-switch cycles.

Written by the indexing model from the issue text.