Orphaned process after closing the code-server browser tab

### Is there an existing issue for this?

- [x] I have searched the existing issues

### OS/Web Information

- Web Browser: edge
- Local OS: windows
- Remote OS: linux
- Remote Architecture: amd64
- `code-server --version`: 4.100.0

### Steps to Reproduce

1. A standard scala project with metals and bloop
2. kick off a run through vscode launch configs
3. close the browser tab

### Expected

All the processes launched by that browser sessions should be killed and cleaned up after the browser closure

### Actual

The process are still running in the background with unclear states, and there is no way to "reconnect" to the orphaned processes

### Logs

```shell

```

### Screenshot/Video

_No response_

### Does this bug reproduce in native VS Code?

No, this works as expected in native VS Code

### Does this bug reproduce in GitHub Codespaces?

I did not test GitHub Codespaces

### Are you accessing code-server over a secure context?

- [x] I am using a secure context.

### Notes

I believe for vscode desktop, closing the editor will close all the "tasks" launched by vscode, but that doesn't appear to be the case for code-server. This applies to all the 3rd party extensions, and it is pretty bad because it basically leaks resources.

Also for certain applications that want to make sure there is only one process running at all time, and failure to clean up the resources actually impacts the functionalities.