Godot Editor is closed when VSCode is closed if opened using "Open workspace with Godot Editor" from VSCode

### Godot version

4.2.1

### VS Code version

VSCodium 1.87.1

### Godot Tools VS Code extension version

2.0.0

### System information

macOS 14.4

### Issue description

If Godot is opened with the "Open workspace with Godot Editor" closing VSCode will also instantly close Godot (discarding any unsaved changes) which is really annoying since VSCode updates often and restarting VSCode in order to update will also close Godot.

This might be a fringe case but it happens to me quite often because the fastest way of opening a project in Godot is to use the "Open workspace with Godot Editor" button in VSCode that shows up when it disconnects from the LSP.

Reasons I use that button daily:
- Godot editor prevents sleep on macOS, so I close it at the end of the day
- Frequently having to restart the editor because of: https://github.com/godotengine/godot/issues/88399
- Godot editor crashes a lot

### Steps to reproduce

- Open your project in the Godot Editor
- Open a script file in VSCode
- Close the Godot Editor
- Click the "Open workspace with Godot Editor" button in the popup that shows up in VSCode
- Wait for Godot to open
- Close VSCode (or restart it because of an update)
- The Godot editor will also close