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The code referred to can be found in AbstractProgressFragment.onResume().

override fun onResume() {
  super.onResume()
  if (navigated) {
    findNavController().popBackStack()
    return
  }
  var monitor = installViewModel.installMonitor
  if (monitor == null) {
    Log.i(TAG, "onResume: monitor is null, navigating")
    navigate()
    monitor = installViewModel.installMonitor
  }
  if (monitor != null) {
    Log.i(TAG, "onResume: monitor is now not null, observing")
    monitor.status.observe(this, StateObserver(monitor))
  }
}

In case no monitor is attached during onResume, we assign the installMonitor from installViewModel.
In either case a new StateObserver is attached, which then observes status changes.
Once SplitSessionInstallState.INSTALLED is observed, navigate() is invoked from within StateObserver.

Since navigate is called in the StateObserver we might see multiple invocations by accident.

To alleviate this, we could create a one shot Event, which would cause the existing API to change.
Alternatively, moving the calls from onResume earlier in the lifecycle, e.g. onCreateView could avoid unnecessary view creation in case navigation already has taken place, and could avoid multiple calls to the observed status.

This has been fixed and will be available in an upcoming Navigation 2.3.2 release.

#4 I think this fix break the behavior of DefaultProgressFragment, it doesn't call super.onViewCreated() so that the installation won't execute.

onViewCreated on Fragment is a GNDN function, so no need to override it.

Can you provide more information as to how your installation won't execute?

Move install monitor observation to onViewCreated

DefaultProgressFragment won't execute super(AbstractProgressFragment)'s onViewCreated(). So after this change, DefaultProgressFragment can't monitor the installation progress.

TL;DR

Call super.onViewCreated(view, savedInstanceState) in DefaultProgressFragment will solve this issue.