Tab switching gets stuck in Settings tab

### Windows Terminal version

1.22.10352.0

### Windows build number

10.0.22635.4870

### Other Software

_No response_

### Steps to reproduce

I have found two bugs that are closely related, as the first one appears during the steps to reproduce the second bug, so I'll put them both together in this issue:

1. Open a new window with 3 tabs: Settings and two shells
2. Activate the _Settings_ tab
3. Press the keyboard shortcut for the action "Next/Previous tab" (usually `Ctrl` + `Tab`) so that you keep `Ctrl` pressed and press `Tab` just once - the next tab will be activated, but the **_Tab switcher_ is not shown** (the first bug)
4. While still keeping `Ctrl` pressed down, press `Tab` once again - the last tab will be activated and this time, the Tab switcher finally shows up
5. While still keeping `Ctrl` pressed down, press `Tab` once again - the _Settings_ tab will be activated back
6. Now finally release the `Ctrl` key
7. Press `Ctrl` + `Tab` again (this time you can release both keys immediately) - nothing happens, **tab switching stopped working altogether**, you have to click anywhere on or around settings options to make it work again (the second bug)

### Expected Behavior

1. The _Tab switcher_ should be shown after the first use of "Next/Previous tab" action when you're on the _Settings_ tab, just like it does when any other shell tab is active
2. When you activate the _Settings_ tab using the "Next/Previous tab" action, it should also be possible to leave the _Settings_ tab the same way without the need to click somewhere first

### Actual Behavior

1. When leaving the Settings tab using the "Next/Previous tab" action, the Tab switcher is shown only after the second use of the action
2. When the Settings tab is activated using the "Next/Previous tab" action, it's not possible to leave it the same way, unless the user clicks anywhere on or around (in blank space or settings text) the settings options

No source file or test is named in the issue. First reproduce the tab-switching sequence on the reported Windows Terminal version, then trace the Settings tab focus and Next/Previous tab handling; done means the tab switcher appears on the first action and Settings can be left by the same shortcut without a click.

Written by the indexing model from the issue text.