Frontend server client tests are failing with most recent Dart SDK

[elliette]

See: https://github.com/dart-lang/webdev/actions/runs/7281930354/job/19843422857?pr=2312

[derekxu16]

I've managed to reproduce this locally. The Bad state: No elements error gets thrown when trying to await stdoutLines.next when the process started above exits immediately.

The way I reproduced this was by running another program with dart run --observe before starting the test. This makes the process started by the test exit immediately with Could not start the VM service: localhost:8181 is already in use.

We need to find out why the process started by the test is exiting immediately on CI.