Python: `vscode-python` breaks running language runtimes

[seeM]

1. Start a Python runtime.
2. Trigger VSCode to restart the language server; a simple way is by changing the selected interpreter with the Python: Select Interpreter command
3. There will be no indication in the UI that the runtime has exited, but the console won't work, and trying to exit the runtime won't work. It'll go through states busy => idle => exited => exiting => exiting => ... and get stuck.

I think the problem relates to how we're integrating with vscode-python (see #652).