Dragging window in F11 Fullscreen makes it movable but fails to exit Fullscreen state (Controls remain hidden)

### Windows Terminal version

1.23.20211.0

### Windows build number

10.0.26200.7628

### Other Software

_No response_

### Steps to reproduce

1. Set `"showTabsFullscreen": true` in `settings.json`.
2. Press **F11** to enter Fullscreen mode.
3. Click and drag the tab strip/title bar.

### Expected Behavior

Standard Windows behavior suggests that dragging a snapped or fullscreen window should trigger a "Restore" event, exiting Fullscreen mode, resizing the window to its previous dimensions, and showing the window controls. (_Alternatively: If Fullscreen is intended to be locked, the window should not be draggable at all_).

### Actual Behavior

1. The window detaches and follows the mouse (is draggable).
2. State persists: The app logic remains in "Fullscreen" mode.
3. UI broken: The window does not resize to its "Restored" dimensions, and the caption buttons remain hidden.
4. Recovery: Pressing **F11** again is required to properly exit this state and restore standard window controls.

https://github.com/user-attachments/assets/ba18b83d-5277-44e2-80e2-0a3e298b67a6

Reproduce the issue with showTabsFullscreen enabled, F11, and dragging the tab strip or title bar. Trace the fullscreen and window-drag handling to determine why the window becomes movable without leaving fullscreen; done means dragging either exits fullscreen and restores dimensions and caption buttons, or the fullscreen window is not draggable.

Written by the indexing model from the issue text.