Add support for "close to tray"

### Windows Terminal version

1.12.10732.0

### Windows build number

19044.1645

### Other Software

_No response_

### Steps to reproduce

Enable "always display icon in system tray" and then close the window of Terminal

### Expected Behavior

Window is closed, but Terminal is still running with icon in system tray (the same behavior for any program in system tray, that's why programs usually have option in Settings to be set to system tray!)
To close Terminal completely you should go to system tray and do it manually with right-click on icon and "close" (or smth)

### Actual Behavior

Despite I have Terminal in system tray, after I close the window... the Terminal is simply completely closed...

Start by tracing the existing “always display icon in system tray” setting and the Windows window-close path. Confirm the expected distinction between closing the window and exiting from the tray, then verify both behaviors with the project’s existing test coverage if available.

Written by the indexing model from the issue text.