[Feature Request]: Autosave the opened Godot Editor instance when closing the IDE

### Godot version

4.7.1.stable

### VS Code version

1.107.0 (OSS, Antigravity IDE 2.1.1)

### Godot Tools VS Code extension version

2.7.1

### System information

Windows 11

### Problem statement

Closing the IDE that connected to a godot instance that was launched by this popup, apparently also close the godot editor without saving it.

### Proposed solution

Automatically save any opened scenes and scripts before it autoclose the Godot Editor

No file or test path is named. Start by tracing how the VS Code extension launches and closes the Godot Editor instance from the popup, then identify where shutdown is handled. Done means opened Godot scenes and scripts are saved before the launched editor is closed.

Written by the indexing model from the issue text.