Multiple running apps not detected when inspector opens

If you open the inspector then start multiple apps they all show up in the embedded inspector view. But if you start multiple apps then open the inspector you only see the currently active app. There appears to be no way to add another without restarting it.

cc @AlexV525

Reproduce the two startup sequences described in the issue using the embedded inspector: open it before starting multiple apps, then start the apps before opening it. Investigate how the Flutter IntelliJ plugin discovers running apps when the inspector opens; done means all already-running apps appear without restarting them.

Written by the indexing model from the issue text.