Make sure we handle the LSP `exit` notification

[JoshuaBatty]

After the client sends a shutdown request to the server, it then sends a final exit notification. The server should then instantly kill the running process so it doesn't remain hanging.

Currently this is implemented behind the scenes in tower-lsp. Just leaving a reminder to handle this case ourselves once we deprecate tower and use our own event loop instead.

https://microsoft.github.io/language-server-protocol/specifications/lsp/3.17/specification/#exit